Electronic Journal of Applied Mathematics
type: channel
description: eISSN: 2980-2474 Publisher: Mersin University Journal name: Electronic Journal of Applied Mathematics Abbreviation: Electron. J. Appl. Math. Parallel title: EJAM Frequency: Quarterly (Mar, Jun, Sep, and Dec) Electronic Journal of Applied Mathematics (Electron. J. Appl. Math.) is a peer reviewed, Open Access journal that provides an advanced forum for studies related to mathematics. All published items, including research articles, have unrestricted access and users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. No submission or processing fees are required.
publisher: Department of Library and Documentation, Mersin University
language: en
publication name: Electronic Journal of Applied Mathematics
issn: 2980-2474
copyright: This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
items: Convergence of physics-informed neural networks for time-fractional diffusion equations via stability and generalization bounds
items: A strategy for inverse source term and the initial data for the time-fractional diffusion equation for the Hyper Bessel operator
items: Well-posedness of a conformable parabolic equation with nonhomogeneous Neumann boundary
items: Fishery model influenced by pollution with optimal harvesting policy
items: The effect of fear on two predator-prey pairs linked by competition
items: Fishery model influenced by global warming with optimal harvesting policy
items: Efficient coupling technique for approximate and exact solutions of nonlinear Caputo fractional differential equations
items: A priori strategy for pseudo-parabolic equations by hybrid regularization method
items: Large deviation principle for stochastic \(p\)-Laplacian reversible Selkov lattice systems
items: Weak solutions of Dirichlet discrete nonlinear problems in a two-dimensional Hilbert space
items: New solitary wave solutions of the Korteweg-de Vries (KdV) equation by new version of the trial equation method
items: Blow-up solutions to the fractional solid fuel ignition model
items: Regularization of nonlocal pseudo-parabolic equation with random noise
items: On maximal solution to a degenerate parabolic equation involving a time fractional derivative
items: Non-uniform trajectory tracking AILC for nonlinear time-varying parameter system with multiple unknown control directions
items: Well-posedness results for a class of nonlinear reaction-diffusion equations with memory
items: A delayed eco-epidemiological prey–predator model and its discrete version under the weak Allee effect
items: Blow-up solutions to logarithmic viscoelastic equations with nonlocal weak damping, delay, and acoustic boundary conditions
items: Some fixed point theorems of Leggett–Williams type for multivalued mappings and applications to second-order differential inclusions
items: Finite time blow-up for an inhomogeneous wave equation with Riemann--Liouville fractional integral
items: Positive eigenvalues for the adjoint of an increasing operator
items: The Continuity by Order Derivative for Conformable Parabolic Equations with Exponential Nonlinearity
items: Analytical Solution of the D-DimensionalKlein-Gordon Equation for Dan-Fan MolecularPotential Using AIM
items: Two-weighted inequalities for maximal commutators in generalized weighted Morrey spaces on spaces of homogeneous type
items: Geometry of Solutions of the Geometric Curve Flows in Space
items: Recovering solution of the reverse nonlinear time fractional diffusion equations with fluctuations data
items: Optical soliton solutions of the generalized sine-Gordon equation
items: The Traveling Wave Solutions to a Variant of the Boussinesq Equation
items: Weak Mean Random Attractor of Reversible Selkov Lattice Systems Driven by Locally Lipschitz Lévy Noises
items: Global Attractors of the Delay 2D Navier-Stokes Equations on Unbounded Channel-Like Domains

Convergence of physics-informed neural networks for time-fractional diffusion equations via stability and generalization bounds
type: item
description: Physics-informed neural networks (PINNs) have emerged as a flexible framework for solving partial differential equations (PDEs), yet rigorous convergence results remain limited for models with nonlocal time dependence. This paper studies PINNs for the time-fractional diffusion equation with the Caputo derivative of order \(\alpha\in(0,1)\). We propose a residual-based PINN formulation and establish a stability-driven error bound: the solution error is controlled by the PDE residual together with the boundary and initial condition residuals. By combining this PDE stability with sampling-based generalization bounds for the empirical PINN loss, we prove convergence of empirical minimizers to the true solution as the number of collocation points increases and the approximation and optimization errors vanish. Numerical experiments with manufactured solutions support the theory and demonstrate accuracy.
subject: Research Article
  topic: section
subject: Physics-informed neural networks
  topic: keywords
subject: time-fractional diffusion
  topic: keywords
subject: Caputo derivative
  topic: keywords
subject: stability estimate
  topic: keywords
subject: generalization error
  topic: keywords
subject: convergence
  topic: keywords
subject: 35R11
  topic: subjects
subject: 35K05
  topic: subjects
subject: 65M12
  topic: subjects
subject: 68T07
  topic: subjects
creator: Phuoc Toan Trinh
creator: Huu Dinh Huynh
rights: Copyright (c) 2025 Trinh Phuoc Toan; Huynh Huuu Dinh (Corresponding Author) https://creativecommons.org/licenses/by/4.0
date: 2025-12-26
publication date: 2025-12-26
starting page: 35
ending page: 55
doi: 10.61383/ejam.202534116

A strategy for inverse source term and the initial data for the time-fractional diffusion equation for the Hyper Bessel operator
type: item
description: In this paper, we investigate the inverse problem of simultaneously identifying the source term and the initial value for a time-fractional diffusion equation involving a Caputo-like hyper-Bessel operator. We first establish the ill-posedness of the problem and derive a conditional stability estimate. To overcome this difficulty, we apply the modified Fractional Landweber regularization method and provide error estimates under a priori parameter choice rules.
subject: Research Article
  topic: section
subject: inverse source problem
  topic: keywords
subject: parabolic equation
  topic: keywords
subject: regularization method
  topic: keywords
subject: error estimate
  topic: keywords
subject: 35K99
  topic: subjects
subject: 47J06
  topic: subjects
subject: 47H10
  topic: subjects
subject: 35K05
  topic: subjects
creator: Viet Tri Vo
rights: Copyright (c) 2025 Vo Viet Tri https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 56
ending page: 66
doi: 10.61383/ejam.202534117

Well-posedness of a conformable parabolic equation with nonhomogeneous Neumann boundary
type: item
description: We study a one dimensional parabolic equation involving a conformable time derivative and nonhomogeneous Neumann boundary data. A weak formulation is introduced in weighted Bochner spaces associated with the natural measure \(d_\beta t=t^{\beta-1}\,dt\), and the conformable derivative is interpreted in a weak sense through a suitable transformation of the time variable. A priori energy estimates are derived for the solution in terms of the initial datum, the source term, and the prescribed boundary flux. Using the change of variables \(\tau=t^\beta/\beta\), the problem is transformed into a classical parabolic problem, which yields the existence of weak solutions. Uniqueness and continuous dependence on the data are then established by energy methods, leading to well-posedness in the sense of Hadamard. Under additional regularity assumptions on the initial and boundary data, higher spatial and temporal regularity of the solution is also obtained.
subject: Research Article
  topic: section
subject: conformable derivative
  topic: keywords
subject: parabolic equation
  topic: keywords
subject: Neumann boundary condition
  topic: keywords
subject: weak solution
  topic: keywords
subject: a priori estimate
  topic: keywords
subject: well-posedness
  topic: keywords
subject: regularity
  topic: keywords
subject: 35K20
  topic: subjects
subject: 35D30
  topic: subjects
subject: 35B30
  topic: subjects
subject: 35B65
  topic: subjects
creator: Ngoc Linh La
rights: Copyright (c) 2025 La Ngoc Linh https://creativecommons.org/licenses/by/4.0
date: 2025-12-28
publication date: 2025-12-28
starting page: 67
ending page: 84
doi: 10.61383/ejam.202534125

Fishery model influenced by pollution with optimal harvesting policy
type: item
description: In this work, we proposed a simplified version of the Gordon-Schaefer model in which the mortality rate of the fish stock biomass and the unit cost of effort are due to aquatic pollution, and harvesting is non-linear. Our dynamic study shows that our system is globally bounded and asymptotically and globally stable under certain conditions around the single interior equilibrium point. We then performed a numerical simulation to validate our theoretical results. Next, we determined the maximum sustainable yield (MSY) and maximum equilibrium yield (MEY), and presented numerical results. Finally, using Pontryagin's maximum principle, we determined the optimal control and performed a numerical simulation.
subject: Research Article
  topic: section
subject: Equilibrium points
  topic: keywords
subject: stability, profit
  topic: keywords
subject: fishing effort
  topic: keywords
subject: MSY
  topic: keywords
subject: MEY
  topic: keywords
subject: pollution
  topic: keywords
subject: 34B05
  topic: subjects
subject: 34B08
  topic: subjects
subject: 34D20
  topic: subjects
subject: 34D23
  topic: subjects
subject: 93D05
  topic: subjects
subject: 49J15
  topic: subjects
subject: 19K15
  topic: subjects
creator: Josué Carlos Israël OULAI
creator: Hypolithe OKOU
creator: David Paul TUO
rights: Copyright (c) 2025 Josué Carlos Israël OULAI (Corresponding Author); Hypolithe OKOU, David Paul TUO https://creativecommons.org/licenses/by/4.0
date: 2025-12-26
publication date: 2025-12-26
starting page: 20
ending page: 34
doi: 10.61383/ejam.202534114

The effect of fear on two predator-prey pairs linked by competition
type: item
description: This paper presents a mathematical model examining the dynamics of a linked predator-prey system that incorporates fear. Here each predator consumes one prey only. and the preys are in competition. The nature of predation is of Holling type II. The principal results explore various aspects , including positivity, boundedness, local and global stability of the coexistence equilibrium point, uniform persistence and Hopf bifurcation. The numerical simulations support the theoretical findings, offering practical insights into the model's behaviour.
subject: Research Article
  topic: section
subject: linked predator-prey system
  topic: keywords
subject: fear factor
  topic: keywords
subject: stability
  topic: keywords
subject: uniform persistence
  topic: keywords
subject: bifurcation
  topic: keywords
subject: 34C23
  topic: subjects
subject: 34D23
  topic: subjects
subject: 37G15
  topic: subjects
subject: 92D25
  topic: subjects
creator: Debasis Mukherjee
rights: Copyright (c) 2025 Debasis Mukherjee https://creativecommons.org/licenses/by/4.0
date: 2025-12-20
publication date: 2025-12-20
starting page: 1
ending page: 19
doi: 10.61383/ejam.202534111

Fishery model influenced by global warming with optimal harvesting policy
type: item
description: In this article, we proposed a modified version of the Gordon-Schaefer model in which harvesting is non-linear and the mortality rate of the fish stock is a function of temperature. We showed that every solution of the system is globally bounded and that there is a single interior equilibrium point that is locally, asymptotically, and globally stable under certain conditions. We then determined the optimal levels of production and profit when the stock evolution is kept constant (MSY and MEY, respectively). Furthermore, using Pontryagin's maximum principle, we characterized the optimal harvesting policy that maximizes net present value. Finally, we performed numerical simulations to validate our theoretical results.
subject: Research Article
  topic: section
subject: equilibrium points
  topic: keywords
subject: stability
  topic: keywords
subject: profit
  topic: keywords
subject: fishing effort
  topic: keywords
subject: MSY
  topic: keywords
subject: MEY
  topic: keywords
subject: temperature
  topic: keywords
subject: 34B05
  topic: subjects
subject: 34B08
  topic: subjects
subject: 34D20
  topic: subjects
subject: 34D23
  topic: subjects
subject: 93D05
  topic: subjects
subject: 49J15
  topic: subjects
subject: 19K15
  topic: subjects
creator: Josué Carlos Israël OULAI
creator: Hypolithe OKOU
creator: Albin Tetchi N'GUESSAN
rights: Copyright (c) 2025 Josué Carlos Israël OULAI (Corresponding Author); Hypolithe OKOU, Albin Tetchi N'GUESSAN https://creativecommons.org/licenses/by/4.0
date: 2025-09-25
publication date: 2025-09-25
starting page: 64
ending page: 82
doi: 10.61383/ejam.202533113

Efficient coupling technique for approximate and exact solutions of nonlinear Caputo fractional differential equations
type: item
description: Complex phenomena such as anomalous diffusion, fractal structures, viscoelasticity, and chaotic dynamics are effectively described using fractional-order nonlinear models. Solving these nonlinear fractional models provides deeper insight into the mechanisms and behaviors underlying such processes. In this work, we develop a hybrid analytical technique for solving nonlinear fractional partial differential equations by coupling the residual function with the Laplace transform, referred to as the Laplace residual power series method (LRPSM). This method is constructed upon a modified fractional-order power series formulated within the framework of the Caputo derivative. The accuracy of the proposed approach is confirmed through absolute, relative, and residual error analyses. LRPSM efficiently determines the coefficients of series solutions using a simple limit principle at infinity, in contrast to well-established methods such as the variational iteration method, Adomian decomposition method, and homotopy perturbation method, which typically require complex integrations. Likewise, the classical residual power series method (RPSM) depends on higher-order derivatives, which become increasingly challenging in fractional settings. Since LRPSM avoids the use of Adomian's or He's polynomials for handling nonlinearities, it proves to be a more straightforward and computationally efficient alternative for obtaining accurate series solutions to nonlinear fractional problems.
subject: Research Article
  topic: section
subject: Fractional nonlinear model
  topic: keywords
subject: Caputo derivative
  topic: keywords
subject: Laplace transform
  topic: keywords
subject: residual function
  topic: keywords
subject: approximate solution
  topic: keywords
subject: closed-form solution
  topic: keywords
subject: 22E70
  topic: subjects
subject: 34A08
  topic: subjects
subject: 35R11
  topic: subjects
creator: Muhammad Imran Liaqat
rights: Copyright (c) 2025 Muhammad Imran Liaqat (Corresponding Author) https://creativecommons.org/licenses/by/4.0
date: 2025-09-25
publication date: 2025-09-25
starting page: 83
ending page: 106
doi: 10.61383/ejam.202533112

A priori strategy for pseudo-parabolic equations by hybrid regularization method
type: item
description: In this study, we address the simultaneous recovery of the source term and the initial value in a time-fractional diffusion equation, a problem inherently characterized by its ill-posed nature. To overcome this challenge, we propose a hybrid regularization method, offering robust solutions and providing precise estimations for both the source term and the initial value.
subject: Research Article
  topic: section
subject: time-fractional diffusion equation
  topic: keywords
subject: inverse source term
  topic: keywords
subject: initial value problem
  topic: keywords
subject: hybrid regularization method
  topic: keywords
subject: priori estimation
  topic: keywords
subject: 35K99
  topic: subjects
subject: 47J06
  topic: subjects
subject: 47H10
  topic: subjects
subject: 35K05
  topic: subjects
creator: Ngo Ngoc Hung
creator: Dinh Long Le
rights: Copyright (c) 2025 Le Dinh Long, Ngo Ngoc Hung https://creativecommons.org/licenses/by/4.0
date: 2025-09-13
publication date: 2025-09-13
starting page: 1
ending page: 20
doi: 10.61383/ejam.202533103

Large deviation principle for stochastic \(p\)-Laplacian reversible Selkov lattice systems
type: item
description: The Selkov system is a classical model for autocatalytic biochemical reactions such as glycolysis and exhibits complex spatio-temporal patterns including self-excitation, oscillations, and spatial chaos. In this paper, we consider stochastic \(p\)-Laplacian reversible Selkov lattice systems defined on the integer set \(\mathbb{Z}\), which possess two pairs of oppositely signed nonlinear terms and whose nonlinear couplings can grow polynomially with any order \(q \geq 1\), the inherent structure of the system precludes the possibility of any unidirectional dissipative influence arising from the interaction between the two coupled equations, thereby obstructing the emergence of a dominant energy-dissipation mechanism along a single directional pathway. In particular, our focus is on studying the asymptotic properties of the \((\psi^\gamma, \phi^\gamma)\) as the noise intensity \(\gamma \to 0\) for the systems. Based on the well-posedness and the convergence of the solutions of the controlled system associated with the considered system, by the weak convergence method, we establish the large deviation principle in \( C([0,T], \ell^2 \times \ell^2) \) for such infinite dimensional system. One of the advantages of the weak convergence method that does not rely on uniform exponential probability estimates of solutions. Moreover, a stopping time technique is used to prove \(\lim\limits_{\gamma \to 0} \left( \psi^\gamma_{z^\gamma} - \psi_{z^\gamma}, \phi^\gamma_{z^\gamma} - \phi_{z^\gamma} \right) = 0\) in probability in order to overcome the difficulty caused by the local monotonicity of the nonlinear and diffusion terms. Compared to the classical case of cubic nonlinearity, our results are not only more general in scope but also demonstrate a higher degree of novelty.
subject: Research Article
  topic: section
subject: Gray-Scott lattice systems
  topic: keywords
subject: Weak convergence
  topic: keywords
subject: Uniform estimate
  topic: keywords
subject: Large deviation
  topic: keywords
subject: 37L40
  topic: subjects
subject: 35B41
  topic: subjects
subject: 37L60
  topic: subjects
subject: 35B40
  topic: subjects
creator: Liguang Zhou
creator: Liheng Liu
creator: Zhenqin Nie
creator: Jibing Leng
rights: Copyright (c) 2025 Liguang Zhou, Liheng Liu, Zhenqin Nie; Jibing Leng (Corresponding Author) https://creativecommons.org/licenses/by/4.0
date: 2025-09-17
publication date: 2025-09-17
starting page: 34
ending page: 63
doi: 10.61383/ejam.202533107

Weak solutions of Dirichlet discrete nonlinear problems in a two-dimensional Hilbert space
type: item
description: In this paper we prove the existence of at least one weak solution of a discrete nonlinear Dirichlet boundary-value problem in a two-dimensional Hilbert space. The main existence results based on variational approach, specially minimization methods.
subject: Research Article
  topic: section
subject: discrete boundary value problem
  topic: keywords
subject: critical point
  topic: keywords
subject: two-dimensional
  topic: keywords
subject: discrete Hilbert space
  topic: keywords
subject: weak solution
  topic: keywords
subject: variational approach
  topic: keywords
subject: 47A75
  topic: subjects
subject: 34B15
  topic: subjects
subject: 35B38
  topic: subjects
subject: 65Q10
  topic: subjects
creator: Kalifa DIANDA
creator: Yassia OUEDRAOGO
creator: Malick ZOUNGRANA
rights: Copyright (c) 2025 A.A.K. Dianda (Corresponding Author); Yassia Ouedraogo, Malick Zoungrana https://creativecommons.org/licenses/by/4.0
date: 2025-09-15
publication date: 2025-09-15
starting page: 21
ending page: 33
doi: 10.61383/ejam.202534100

New solitary wave solutions of the Korteweg-de Vries (KdV) equation by new version of the trial equation method
type: item
description: New solitary wave solutions for the Korteweg-de Vries (KdV) equation by a new version of the trial equation method are attained. Proper transformation reduces the Korteweg-de Vries (KdV) equation to a quadratic ordinary differential equation that is fully integrated using the new version trial equation approach. The family of solitary wave solutions of the reduced equation ensures a combined expression for the Korteweg-de Vries (KdV) equation, which contains exact solutions derived in recent years using different integration methods. The analytic solution of the reduced equation permits to find exact solutions for the Korteweg-de Vries (KdV) equation, providing a variety of new solitary wave solutions that have not been reported before.
subject: Research Article
  topic: section
subject: New version of the trial equation method
  topic: keywords
subject: nonlinear partial differential equations
  topic: keywords
subject: Korteweg-de Vries (KdV) equation
  topic: keywords
subject: solitary wave soliton solutions
  topic: keywords
creator: Yusuf Pandir
creator: Ali Ekin
rights: Copyright (c) 2023 Yusuf Pandir (Corresponding Author); Ali Ekin https://creativecommons.org/licenses/by/4.0
date: 2023-05-09
publication date: 2023-05-09
starting page: 101
ending page: 113
doi: 10.61383/ejam.20231130

Blow-up solutions to the fractional solid fuel ignition model
type: item
description: In this study, we investigate a time fractional parabolic equation with Caputo-Fabrizio derivative and a pure exponential source term. The model can be seen as a modified version of a solid fuel ignition by considering delay effects. Because of the bad behavior of the source term, the common Banach fixed point theorem is not suitable to be applied. Therefore, we approach by an iteration method in which we find a supersolution to the problem. Then, the monotony of approximating solutions implies the existence of a mild solution. Furthermore, we show that if the given initial data is sufficiently large in term of norm measure, the corresponding solution will blow up in a finite time. Main techniques of the work are mainly based on calculations related to explicit formulas of solution operator derived from eigenpair of Helmholtz's equation and Sobolev embeddings between Hilbert scale spaces.
subject: Research Article
  topic: section
subject: Caputo-Fabrizio
  topic: keywords
subject: fractional equation
  topic: keywords
subject: exponential nonlinearity
  topic: keywords
creator: Nguyen Dinh Huy
creator: Anh Tuan Nguyen
rights: Copyright (c) 2023 Nguyen Dinh Huy; Anh Tuan Nguyen (Corresponding Author) https://creativecommons.org/licenses/by/4.0
date: 2023-05-07
publication date: 2023-05-07
starting page: 30
ending page: 39
doi: 10.61383/ejam.20231126

Regularization of nonlocal pseudo-parabolic equation with random noise
type: item
description: In this paper, we consider an inverse problem for a time-fractional diffusion equation with the inhomogeneous source. These problems have many applications in engineering such as image processing, geophysics, biology. We get the result in random case as follows: • This problem is ill-posed. • We have used the nonlocal condition, instead of the final time condition. • Using the IFT regularization method, constructing the regularized solution, the a-priori choice rule for the regularization parameter is discussed and yields the corresponding convergence rate. • A numerical experiment is presented to illustrate the results in theory.
subject: Research Article
  topic: section
subject: Fractional Tikhonov
  topic: keywords
subject: Regularization
  topic: keywords
subject: Conformable time derivative
  topic: keywords
subject: Discrete data
  topic: keywords
subject: random noise
  topic: keywords
subject: 35K99
  topic: subjects
subject: 47J06
  topic: subjects
subject: 47H10
  topic: subjects
subject: 35K05
  topic: subjects
creator: Yusuf Gurefe
creator: Dinh Long Le
creator: Devendra Kumar
rights: Copyright (c) 2023 Yusuf Gurefe; Le Dinh Long (Corresponding Author); Devendra Kumar https://creativecommons.org/licenses/by/4.0
date: 2023-05-08
publication date: 2023-05-08
starting page: 40
ending page: 61
doi: 10.61383/ejam.20231119

On maximal solution to a degenerate parabolic equation involving a time fractional derivative
type: item
description: In this paper, we consider a degenerate parabolic equation associated with Caputo derivative. Our problem is studied in the unbounded domain and the nonlocal initial condition. Under some suitable conditions of the input data, we show the local existence of the mild solution. Then we show the continuation of the mild solution. We also claim the maximal mild solution. The main analysis in the current paper is based on some estimations of resolvent theory combined with many complex valuations on solutions operators in Banach spaces.
subject: Research Article
  topic: section
subject: degenerate parabolic equation, fractional integrodifferential equation, mild solution, maximal solution
  topic: keywords
creator: Bui Dai Nghia
creator: Nguyen Hoang Luc
creator: Xiaolan Qin
creator: Yan Wang
rights: Copyright (c) 2023 Bui Dai Nghia; Nguyen Hoang Luc (Corresponding Author); Xiaolan Qin, Yan Wang https://creativecommons.org/licenses/by/4.0
date: 2023-05-08
publication date: 2023-05-08
starting page: 62
ending page: 80
doi: 10.61383/ejam.20231129

Non-uniform trajectory tracking AILC for nonlinear time-varying parameter system with multiple unknown control directions
type: item
description: In this paper, a new iterative learning controller is presented for nonlinear time-varying parameter system to solve the tracking problem of different target trajectories. Based on Nussbaum function and the Lyapunov-like synthesis design the learning controller to handle system dynamics with multi-unknown control directions. Over a finite time interval, the unknown time-varying parameter is considered to be periodic, so it is expanded using a Fourier series expansion, and the remaining terms are treated with a canonical series. The controller designed in this paper can ensure that all signals of the closed-loop system are bounded in a finite time interval [0,T], and can complete non-uniform target tracking. Finally, a simulation example is given to verify the effectiveness of the designed controller.
subject: Research Article
  topic: section
subject: Iterative learning control
  topic: keywords
subject: Time-varying parameter systems
  topic: keywords
subject: Lyapunov-like
  topic: keywords
subject: Multiple unknown control directions
  topic: keywords
subject: Non-uniform target tracking
  topic: keywords
subject: 60G15
  topic: subjects
subject: 60G22
  topic: subjects
subject: 60G52
  topic: subjects
creator: Chunli Zhang
creator: Yangjie Gao
creator: Lei Yan
rights: Copyright (c) 2023 Chunli Zhang (Corresponding Author); Yangjie Gao, Lei Yan https://creativecommons.org/licenses/by/4.0
date: 2023-05-09
publication date: 2023-05-09
starting page: 81
ending page: 100
doi: 10.61383/ejam.20231127

Well-posedness results for a class of nonlinear reaction-diffusion equations with memory
type: item
description: In this paper, we are interested to study the initial value problem for nonlinear heat equation with memory. For our problem, we show that the local existence theory related to the finite time blow-up is also obtained for the problem with logarithmic nonlinearity. We also obtain the blowup continuation property of the mild solution. The principal techniques based on some Sobolev embeddings with \(L^p\) spaces.
subject: Research Article
  topic: section
subject: nonlinear heat equation
  topic: keywords
subject: reaction-diffusion equations
  topic: keywords
subject: memory term
  topic: keywords
subject: blow-up
  topic: keywords
creator: Duy Binh Ho
creator: Duc Phuong Nguyen
creator: Viet Tri Vo
rights: Copyright (c) 2023 Ho Duy Binh; Nguyen Duc Phuong (Corresponding Author); Vo Viet Tri https://creativecommons.org/licenses/by/4.0
date: 2023-05-07
publication date: 2023-05-07
starting page: 1
ending page: 29
doi: 10.61383/ejam.20231125

A delayed eco-epidemiological prey–predator model and its discrete version under the weak Allee effect
type: item
description: This study looks into a delayed predator–prey model that includes competition within the hunter species and a strong Allee effect in the prey population. The time delay is used as a bifurcation measure to look at how stable the coexistence equilibrium is. Our findings show that a Hopf splitting can happen when the delay goes over a certain level. The normal for \(m\) theory and center manifold method is used to find the direction and stability of the periodic solutions that are made. Number simulations add to the evidence for the mathematical findings.
subject: Research Article
  topic: section
subject: Allee-effect
  topic: keywords
subject: Stability
  topic: keywords
subject: Hopf-bifurcation
  topic: keywords
subject: Intra-specific competition
  topic: keywords
subject: 34D20
  topic: subjects
subject: 34C23
  topic: subjects
subject: 37J70
  topic: subjects
creator: Kalyan Das
creator: Kumar G.Ranjith
rights: Copyright (c) 2025 Kalyan Das (Corresponding Author); G.Ranjith Kumar https://creativecommons.org/licenses/by/4.0
date: 2025-06-23
publication date: 2025-06-23
starting page: 49
ending page: 64
doi: 10.61383/ejam.20253260

Blow-up solutions to logarithmic viscoelastic equations with nonlocal weak damping, delay, and acoustic boundary conditions
type: item
description: We in this paper consider the blow-up behavior of any nontrivial solution to the following initial boundary value problem of the logarithmic viscoelastic equations with delay and nonlocal weak damping terms under acoustic boundary conditions \[\begin{aligned} u_{tt} - \Delta u + \|u_t\|^k_2u_t &+ \int^t_0\omega(t-s)\Delta u(s)ds +c_1|u_t(t)|^{m-2}u_t(t)\\ & +c_2|u_t(t-\tau)|^{m-2}u_t(t-\tau) =|u|^{p-2}u\ln |u|. \end{aligned} \] Our results show that the local solution blows up in finite time if $p > m$ and $E(0) < 0$. More accurately, we give the upper bound of the blow-up time by the energy method. Moreover, we also give the lower bound of the blow-up time.
subject: Research Article
  topic: section
subject: Finite time blow-up
  topic: keywords
subject: Logarithmic viscoelastic equations
  topic: keywords
subject: Nonlocal weak damping term
  topic: keywords
subject: Time delay
  topic: keywords
subject: Acoustic boundary conditions
  topic: keywords
subject: 35B44
  topic: subjects
subject: 35D30
  topic: subjects
subject: 35L05
  topic: subjects
subject: 35L70
  topic: subjects
creator: 倩倩 罗
creator: 霁松 段
rights: Copyright (c) 2025 Qianqian Luo; Jisong Duan (Corresponding Author) https://creativecommons.org/licenses/by/4.0
date: 2025-06-15
publication date: 2025-06-15
starting page: 1
ending page: 15
doi: 10.61383/ejam.202532102

Some fixed point theorems of Leggett–Williams type for multivalued mappings and applications to second-order differential inclusions
type: item
description: This paper examines the application of fixed point index theory to set-valued mappings in ordered Banach spaces, with a specific focus on Leggett-Williams type fixed point theorems. The study provides novel conditions for the existence of one and multiple fixed points under a range of assumptions. Additionally, it applies these results to prove the existence of positive solutions for the second-order differential inclusion problem \( - x''(t) \in f\left( {t,x(t)} \right),t \in [0,1]\) with boundary conditions \(x(0)=0=x'(1)\). The obtained results contribute to expanding the scope of application of fixed point theory, providing new techniques for solving boundary value problems in different cases.
subject: Research Article
  topic: section
subject: fixed point index
  topic: keywords
subject: fixed point theorem of Leggett--Williams type
  topic: keywords
subject: multivalued mapping
  topic: keywords
subject: second-order differential inclusions
  topic: keywords
subject: 37C25
  topic: subjects
subject: 47H04
  topic: subjects
subject: 47H10
  topic: subjects
creator: Quang ND
rights: Copyright (c) 2025 Nguyen Dang Quang https://creativecommons.org/licenses/by/4.0
date: 2025-06-20
publication date: 2025-06-20
starting page: 16
ending page: 29
doi: 10.61383/ejam.202532104

Finite time blow-up for an inhomogeneous wave equation with Riemann--Liouville fractional integral
type: item
description: This paper is devoted to the study of the effect of an inhomogeneity \( \omega(x) \) on the blow-up phenomena for the wave equation \[ u_{tt} - \triangle u = I_{0^{+}}^{\alpha}(|u|^{p}) + \omega(x), \quad (t,x) \in (0,T) \times \mathbb{R}^{N}, \]where \( N \ge 1 \), \( p > 1 \), \( 0 \le \alpha < 1 \), and \( \omega(x) \) satisfies \( \int_{\mathbb{R}^{N}} \omega(x)\,dx > 0 .\) Specifically, by the method of cut-functions, this paper first proves that any non-trivial solution blows up in finite time under \( 0 < \alpha < 1 \), and later proves that any non-trivial solution blows up in finite time under \( \alpha = 0 \), \( 2 \le N \le 4 \), and \( p \) being the Strauss exponent.
subject: Research Article
  topic: section
subject: Finite time blow-up
  topic: keywords
subject: Inhomogeneous wave equation
  topic: keywords
subject: Riemann-Liouville fractional integral
  topic: keywords
subject: Strauss exponent
  topic: keywords
subject: 35B44
  topic: subjects
subject: 35L10
  topic: subjects
creator: changyong Xiang
creator: Jisong Duan
creator: Qianqian Luo
rights: Copyright (c) 2025 Changyong Xiang (Corresponding Author); Jisong Duan, Qianqian Luo https://creativecommons.org/licenses/by/4.0
date: 2025-06-22
publication date: 2025-06-22
starting page: 38
ending page: 48
doi: 10.61383/ejam.202532105

Positive eigenvalues for the adjoint of an increasing operator
type: item
description: This paper develops a general framework for investigating the eigenvalue problem of the extended adjoint mapping \(A^\ast:E_b^\ast\to E_b^\ast\) associated with a possibly nonlinear operator \(A:E\to E\). By employing the theory of relative topological degree for condensing mappings with respect to a measure of noncompactness, we establish sufficient conditions ensuring the existence of positive eigenvalues of \(A^\ast\). The extended dual space \(E_b^\ast\) is strictly larger than the classical dual \(E^\ast\), and the two coincide only when \(E\) is finite-dimensional. In this special case, our results recover the classical eigenvalue theory for linear compact operators. The framework introduced here extends the topological degree approach to a broader nonlinear setting and provides a foundation for further applications to convex processes and control problems.
subject: Research Article
  topic: section
subject: eigenvalue
  topic: keywords
subject: eigenvector
  topic: keywords
subject: eigen-pair
  topic: keywords
subject: fixed point index
  topic: keywords
subject: dual operator
  topic: keywords
subject: 47H04
  topic: subjects
subject: 47H07
  topic: subjects
subject: 47H10
  topic: subjects
subject: 35P30
  topic: subjects
creator: Nguyen Hoang Tuan
creator: Vo Viet Tri
creator: Anh Tuan Nguyen
rights: Copyright (c) 2025 Nguyen Hoang Tuan, Vo Viet Tri; Nguyen Anh Tuan (Corresponding Author) https://creativecommons.org/licenses/by/4.0
date: 2025-06-21
publication date: 2025-06-21
starting page: 30
ending page: 37
doi: 10.61383/ejam.202532109

The Continuity by Order Derivative for Conformable Parabolic Equations with Exponential Nonlinearity
type: item
description: In this article, we examine the continuity according to the derivative order of conformable parabolic equations. We establish the existence and uniqueness of mild solutions to the problem of source function exponential non-linearity. We prove the existence and uniqueness of a mild solution based on some Sobolev embeddings, the Banach space of all continuous functions, and the Banach fixed point theorem. In addition, we will address the nonlinear model's continuity issue and demonstrate the mild solution's convergence to the nonlinear problem when \(\gamma'\to \gamma\).
subject: Research Article
  topic: section
subject: initial value problem
  topic: keywords
subject: Sobolev embeddings
  topic: keywords
subject: parabolic equations
  topic: keywords
subject: exponential non-linearity
  topic: keywords
subject: conformable derivative
  topic: keywords
subject: 35K20
  topic: subjects
subject: 35R11
  topic: subjects
creator: Binh Ho Duy
creator: Dinh Huy Nguyen
creator: Tien Nguyen Van
creator: Dang Khoa Le
rights: Copyright (c) 2025 Ho Duy Binh, Nguyen Dinh Huy; Nguyen Van Tien (Corresponding Author); Le Dang Khoa https://creativecommons.org/licenses/by/4.0
date: 2025-03-28
publication date: 2025-03-28
starting page: 42
ending page: 63
doi: 10.61383/ejam.202531101

Analytical Solution of the D-DimensionalKlein-Gordon Equation for Dan-Fan MolecularPotential Using AIM
type: item
description: In this article, the D-dimensional Klein-Gordon equation within the framework of improved Greene-Aldrich approximations scheme for Deng-Fan molecular potential is solved for s-wave and arbitrary angular momenta. The energy eigenvalues and corresponding wave functions are obtained in an exact analytical manner by using asymptotic iteration method.
subject: Research Article
  topic: section
subject: Deng-Fan molecular potential
  topic: keywords
subject: improved Greene-Aldrich approximation scheme
  topic: keywords
subject: asymptotic iteration method (AIM)
  topic: keywords
subject: 81V45
  topic: subjects
subject: 81V73
  topic: subjects
subject: 92F05
  topic: subjects
subject: 93B60
  topic: subjects
creator: Bijon Biswas
rights: Copyright (c) 2025 Bijon Biswas https://creativecommons.org/licenses/by/4.0
date: 2025-03-22
publication date: 2025-03-22
starting page: 34
ending page: 41
doi: 10.61383/ejam.20253158

Two-weighted inequalities for maximal commutators in generalized weighted Morrey spaces on spaces of homogeneous type
type: item
description: In this paper we give a characterization of two-weighted inequalities for maximal commutators in generalized weighted Morrey spaces on spaces of homogeneous type \(\mathcal{M}_{\omega }^{p,\varphi }(X)\). We prove the boundedness of maximal commutators \([M,b]\) from the spaces \(\mathcal{M}_{\omega _{1}^{\delta }}^{p,\varphi _{1}}(X)\) to the spaces \(\mathcal{M}_{\omega _{2}^{\delta }}^{p,\varphi _{2}}(X)\), where \(1<p<\infty \), \(0<\delta <1\) and \((\omega _{1},\omega _{2})\in \widetilde{A}_{p}(X)\).
subject: Research Article
  topic: section
subject: Maximal operator
  topic: keywords
subject: commutator
  topic: keywords
subject: generalized weighted Morrey space
  topic: keywords
subject: spaces of homogeneous type
  topic: keywords
creator: Ayşenur Aydoğdu
creator: Canay Aykol
creator: Javanshir J. Hasanov
rights: Copyright (c) 2023 Ayşenur Aydoğdu; Canay Aykol (Corresponding Author); Javanshir J. Hasanov https://creativecommons.org/licenses/by/4.0
date: 2023-09-09
publication date: 2023-09-09
starting page: 18
ending page: 28
doi: 10.61383/ejam.20231235

Geometry of Solutions of the Geometric Curve Flows in Space
type: item
description: In this study, we aim at investigating the geometry of surfaces corresponding to the geometry of solutions of the geometric curve flows in Euclidean 3-space \(\mathbb R^3\) considering the Frenet frame. In particular, we express some geometric properties and some characterizations of \(u\)-parameter curves and \(t\)-parameter curves of some trajectory surfaces including the Hasimoto surface, the shortening trajectory surface, the minimal trajectory surface, the \(\sqrt{\tau}\)-normal trajectory surface in \(\mathbb R^3\).
subject: Research Article
  topic: section
subject: the Hasimoto surface
  topic: keywords
subject: the shortening trajectory surface
  topic: keywords
subject: the minimal trajectory surface
  topic: keywords
subject: the \(\sqrt{\tau}\)-normal trajectory surface
  topic: keywords
creator: Zehui Zhao
creator: Shiping Zhong
creator: Xinjie Wan
rights: Copyright (c) 2023 Zehui Zhao; Shiping Zhong (Corresponding Author); Xinjie Wan https://creativecommons.org/licenses/by/4.0
date: 2023-10-29
publication date: 2023-10-29
starting page: 16
ending page: 25
doi: 10.61383/ejam.20231340

Recovering solution of the reverse nonlinear time fractional diffusion equations with fluctuations data
type: item
description: In this study, our focus is on obtaining an estimated solution for the nonlinear fractional time diffusion equation. Specifically, we have utilized the Riemann Liouville fractional derivative. Additionally, we have concerned Gaussian white noise in the input data. As we are aware, this problem is considered ill-posed according to Hadamard's definition. To tackle this problem, we have proposed a regularized solution and demonstrated the convergence between the mild solution and the regularized solution.
subject: Research Article
  topic: section
subject: Riemann-Liouville
  topic: keywords
subject: Regularized solution
  topic: keywords
subject: Gaussian white noise
  topic: keywords
subject: Ill-posed
  topic: keywords
creator: Thanh Xuan Doan Thi
creator: Thanh Ha Vo Thi
rights: Copyright (c) 2023 Doan Thi Thanh Xuan; Vo Thi Thanh Ha (Corresponding Author) https://creativecommons.org/licenses/by/4.0
date: 2023-09-09
publication date: 2023-09-09
starting page: 60
ending page: 70
doi: 10.61383/ejam.20231237

Optical soliton solutions of the generalized sine-Gordon equation
type: item
description: In this study, the extended trial equation method based on the general form of the nonlinear elliptic ordinary differential equation is employed to solve the nonlinear generalized sine-Gordon equations. By using this method, we achieve, unlike new types of exact wave solutions such as Elliptic-F, Elliptic-E, and Elliptic-Π functions that are known as elliptic integrals.
subject: Research Article
  topic: section
subject: trial equation method
  topic: keywords
subject: elliptic function solution
  topic: keywords
subject: soliton solution
  topic: keywords
creator: Yusuf Pandir
creator: Humaira Yasmin
rights: Copyright (c) 2023 Yusuf Pandir; Humaira Yasmin (Corresponding Author) https://creativecommons.org/licenses/by/4.0
date: 2023-09-09
publication date: 2023-09-09
starting page: 71
ending page: 86
doi: 10.61383/ejam.20231239

The Traveling Wave Solutions to a Variant of the Boussinesq Equation
type: item
description: In this study, we study a variant of the Boussinesq equation called as \(B( n+1,\,1,\,n )\) equation, and construct some traveling wave solutions by using an effective approach called the extended trial equation method. Thus, the soliton solutions, rational function solutions, elliptic function solutions and Jacobi elliptic function solutions, which show the existence of various mathematical and physical structures and events in the fundamental equation considered, have been constructured. In order to make a more detailed examination of the physical behavior of these solutions, two- and three-dimensional graphs of some solution functions were drawn with the help of the Mathematica package program. In the section of Discussion, we suggest a more general version of the trial equation method for nonlinear differential equations.
subject: Research Article
  topic: section
subject: the extended trial equation method
  topic: keywords
subject: B( n+1,1,n ) equations
  topic: keywords
subject: soliton solution
  topic: keywords
subject: elliptic solutions
  topic: keywords
creator: Muhammad Nadeem
creator: Loredana Florentina Iambor
rights: Copyright (c) 2023 Muhammad Nadeem (Corresponding Author); Loredana Florentina Iambor https://creativecommons.org/licenses/by/4.0
date: 2023-12-24
publication date: 2023-12-24
starting page: 26
ending page: 37
doi: 10.61383/ejam.20231347

Weak Mean Random Attractor of Reversible Selkov Lattice Systems Driven by Locally Lipschitz Lévy Noises
type: item
description: This paper is concerned with weak pullback mean random attractor of reversible Selkov lattice systems defined on the entire integer set \(\mathbb{Z}\) driven by locally Lipschitz Lévy noises. Firstly, we formulate the stochastic lattice equations to an abstract system defined in the non-concrete space \(\ell^2\times\ell^2\) of square-summable sequences. Secondly, we establish the global well-posedness of the systems with locally Lipschitz diffusion terms. Under certain conditions, we show that the long-time dynamics can be captured by a weakly compact and weakly attracting mean random attractor in the Bochner space \(L^2(\Omega,\ell^2\times\ell^2)\). To overcome the difficulty caused by the drift and diffusion terms, we adopt a stopping time technique to prove the convergence of solutions in probability. The mean random dynamical systems theory proposed by Wang (J. Differ. Equ., 31:2177-2204, 2019) is used to deal with the difficulty caused by the nonlinear noise.
subject: Research Article
  topic: section
subject: Selkov systems
  topic: keywords
subject: Weak pullback mean random attractor
  topic: keywords
subject: Lévy noises
  topic: keywords
subject: 35B41
  topic: subjects
subject: 37L40
  topic: subjects
subject: 37B55
  topic: subjects
subject: 37L60
  topic: subjects
subject: 35B40
  topic: subjects
creator: Guofu Li
creator: Xiulan Yang
creator: Liguang Zhou
creator: Yan Wang
rights: Copyright (c) 2024 Guofu Li, Xiulan Yang, Liguang Zhou; Yan Wang (Corresponding Author) https://creativecommons.org/licenses/by/4.0
date: 2024-03-25
publication date: 2024-03-25
starting page: 40
ending page: 63
doi: 10.61383/ejam.20242165

Global Attractors of the Delay 2D Navier-Stokes Equations on Unbounded Channel-Like Domains
type: item
description: This paper studies the global attractors of 2D Navier-Stokes equations with delay defined in unbounded Channel-like domains. We establish the uniform tail-ends estimates of the solutions by establishing all the solutions are uniformly small for overcome the non-compactness of the solutions.
subject: Research Article
  topic: section
subject: Navier-Stokes equations
  topic: keywords
subject: global attractors
  topic: keywords
subject: uniform tail-ends estimates
  topic: keywords
subject: 35B40
  topic: subjects
subject: 35B41
  topic: subjects
creator: Zhang Zhang
creator: Xiaobin Yao
rights: Copyright (c) 2024 Zhang Zhang, Xiaobin Yao (Corresponding Author) https://creativecommons.org/licenses/by/4.0
date: 2024-03-23
publication date: 2024-03-23
starting page: 30
ending page: 39
doi: 10.61383/ejam.20242157