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: 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: A Priori Strategy for Pseudo-Parabolic Equations by Hybrid Regularization Method
items: The Continuity by Order Derivative for Conformable Parabolic Equations with Exponential Nonlinearity
items: Weak Solutions of Dirichlet Discrete Nonlinear Problems in a Two-Dimensional Hilbert Space
items: Analytical Solution of the D-DimensionalKlein-Gordon Equation for Dan-Fan MolecularPotential Using AIM
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: New Solitary Wave Solutions of the Korteweg-de Vries (KdV) Equation by New Version of the Trial Equation Method
items: Well-Posedness Results for a Class of Nonlinear Reaction-Diffusion Equations with Memory
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
items: Dynamics of a Diffusive Two Predators-One Prey System
items: Analytical Solutions of the D-Dimensional Klein-Gordon Equation with Q-Deformed Modified Pöschl-Teller Potential
items: On the Existence of Flux as a Function of the Surface Elevation for Long Wave Solution of Shallow Water Equations
items: Dynamics of a Two Competing Prey-One Predator System with Fear Effect and Anti-Predator Behaviour
items: Existence of Solutions for a Class of Kirchhoff-Type Equations with Indefinite Potential
items: Exponential Stability of Viscoelastic Structure with Second Sound
items: Discrete Multiparameters Potential Boundary Value Problems Involving the \(p(k)\)-Kirchhoff Equations
items: On the Convergence Result for Pseudo-Parabolic Equations with Fractional Time Derivatives
items: Asymptotic Behavior for Delay 2D Navier-Stokes Equations on Unbounded Channel-Like Domains

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

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

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

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; critical point; two-dimensional discrete Hilbert space; weak solution; variational approach.
  topic: keywords
subject: 47A75, 34B15, 35B38, 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

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

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

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

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

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

Dynamics of a Diffusive Two Predators-One Prey System
type: item
description: This paper analyses a diffusive predator-prey model consisting of a single prey species and two predator species with modified Leslie-Gower term Holling type II functional response subject to the homogeneous Neumann boundary condition. Local stability condition is derived by the application of Routh-Hurwitz criterion. Global asymptotic stability of the unique positive steady state is shown by constructing a suitable Lyapunov function when self diffusion is allowed where as non-constant positive steady states can exist due to the presence of cross-diffusion, that means, cross-diffusion can induce stationary pattern. Taking the cross diffusion as a bifurcation parameter, one can show the existence of positive non-constant solutions with the help of bifurcation theory. A brief conclusion completes the paper.
subject: Research Article
  topic: section
subject: Cross-diffusion
  topic: keywords
subject: Leslie-Gower model
  topic: keywords
subject: global stability
  topic: keywords
subject: priori estimates
  topic: keywords
subject: bifurcation
  topic: keywords
creator: Debasis Mukherjee
rights: Copyright (c) 2023 Debasis Mukherjee https://creativecommons.org/licenses/by/4.0
date: 2023-12-28
publication date: 2023-12-28
starting page: 47
ending page: 60
doi: 10.61383/ejam.20231349

Analytical Solutions of the D-Dimensional Klein-Gordon Equation with Q-Deformed Modified Pöschl-Teller Potential
type: item
description: In this article, the D-dimensional Klein-Gordon equation within the framework of Greene-Aldrich approximations scheme for q-deformed modified P¨oschl-Teller Potential is solved for s-wave and arbitrary angular momenta. The energy eigenvalues and corresponding wave functions are obtained in an exact analytical manner via the Nikiforov-Uvarov (N-U) method. Further, it is shown that in the non-relativistic limit, the energy eigenvalues reduce to that of Schrodinger equations for the potential. It is also shown that, the obtained results lead to the solutions of the same problem for modified P¨oschl-Teller potential for \(q = 1\).
subject: Research Article
  topic: section
subject: q-deformed modified P¨oschl-Teller potential, Greene-Aldrich approxi15 mation, Nikiforov-Uvarov (N-U) method
  topic: keywords
creator: Bijon Biswas
rights: Copyright (c) 2024 Bijon Biswas https://creativecommons.org/licenses/by/4.0
date: 2024-03-22
publication date: 2024-03-22
starting page: 14
ending page: 21
doi: 10.61383/ejam.20242156

On the Existence of Flux as a Function of the Surface Elevation for Long Wave Solution of Shallow Water Equations
type: item
description: The shallow water equations in mechanics of fluids, govern the motion of a shallow layer of water over a fixed impervious bed. In this paper, the bed form is assumed to be rough and horizontal, and the motion of water is assumed to be of the long wave type (Lamb [1], pp. 254-256) such that the free surface has a gradually varying propagating profile. Gravitation permits such motion but is resisted by the turbulence generated by the bed friction. A model of the governing equations based on the Reynolds averaged Navier-Stokes equations has recently been given by Bose [2], which is highly nonlinear. A heuristic approach of numerically solving the equations for the modified long waves is also presented in that article, by assuming that the horizontal flux across a section of flow is some function of the free surface elevation alone. This key assertion is analysed in this article and proved to hold provided some boundedness criteria are satisfied by the flux gradients. The theory is apparently applicable to find appropriate boundedness conditions on the flux of flow for numerically solving long wave equations in the case of other models for long wave propagation as well.
subject: Research Article
  topic: section
subject: Shallow water equations
  topic: keywords
subject: turbulence
  topic: keywords
subject: horizontal flux
  topic: keywords
subject: surface elevation
  topic: keywords
creator: Sujit K Bose
creator: Ganesh C Gorain
rights: Copyright (c) 2024 Sujit K.Bose; Ganesh C. Gorain (Corresponding Author) https://creativecommons.org/licenses/by/4.0
date: 2024-03-23
publication date: 2024-03-23
starting page: 22
ending page: 29
doi: 10.61383/ejam.20242154

Dynamics of a Two Competing Prey-One Predator System with Fear Effect and Anti-Predator Behaviour
type: item
description: This paper examines the effect of fear and anti-predator behaviour in a two competing prey and one predator system. Here, one of the competing prey species is affected by the fear of predators while the other competing prey species shows anti-predator behaviour. Basic results on positivity, the boundedness of the solutions, local and global stability of the coexistence equilibrium point, uniform persistence, Hopf bifurcation and the nature of the limit cycle emerging through Hopf bifurcation are investigated. Numerical examples are provided to support our obtained results.
subject: Research Article
  topic: section
subject: Predator-prey model
  topic: keywords
subject: fear factor
  topic: keywords
subject: anti-predator behaviour
  topic: keywords
subject: stability
  topic: keywords
subject: uniform persistence
  topic: keywords
subject: bifurcation
  topic: keywords
subject: 34A34
  topic: subjects
subject: 34C23
  topic: subjects
subject: 37C75
  topic: subjects
subject: 92D25
  topic: subjects
creator: Debasis Mukherjee
rights: Copyright (c) 2024 Debasis Mukherjee https://creativecommons.org/licenses/by/4.0
date: 2024-12-20
publication date: 2024-12-20
starting page: 51
ending page: 65
doi: 10.61383/ejam.20242466

Existence of Solutions for a Class of Kirchhoff-Type Equations with Indefinite Potential
type: item
description: This study explores the existence of solutions to the following Kirchhoff-type problem \[ \left\{ \begin{array} [c]{ll}% -\left(a+b\int_{\mathbb{R}^3}|\nabla u|^2dx\right)\Delta u+ V(x)u=f(x,u),~{\rm{in}}~ \mathbb{R}^{3},\\ u\in H^1(\mathbb{R}^3),% \end{array} % \right. \] where a and b are postive constants, and the potential \(V(x)\) is continuous and indefinite in sign. With suitable assumptions on \(V(x)\) and \(f\), we establish the existence of solutions using the Symmetric Mountain Pass Theorem.
subject: Research Article
  topic: section
subject: Kirchhoff-type equations
  topic: keywords
subject: (C)_c-condition
  topic: keywords
subject: Symmetric Mountain Pass Theorem
  topic: keywords
subject: 35J20
  topic: subjects
subject: 35J50
  topic: subjects
subject: 38E05
  topic: subjects
creator: linlian Xiao
creator: Jiaqian Yuan
creator: Jian Zhou
creator: Yunshun Wu
rights: Copyright (c) 2024 Linlian Xiao, Jiaqian Yuan; Jian Zhou (Corresponding Author); Yunshun Wu https://creativecommons.org/licenses/by/4.0
date: 2024-09-09
publication date: 2024-09-09
starting page: 42
ending page: 50
doi: 10.61383/ejam.20242368

Exponential Stability of Viscoelastic Structure with Second Sound
type: item
description: This manuscript deals with a thermo-viscoelastic system describing the vibrations of a flexible structure. We study this structure's stabilization problem when subjected to Kelvin-Voigt damping and the second sound. Cattaneo-Vernotte's law governs the thermal effect, eliminating the physical paradox of equal speed of waves in the classical thermoelastic theory. Semigroup theory proves the solution's existence and uniqueness. Exponential stability is proved by the energy method.
subject: Research Article
  topic: section
subject: Viscoelastic structure
  topic: keywords
subject: Cattaneo’s law
  topic: keywords
subject: existence of solution
  topic: keywords
subject: exponential decay
  topic: keywords
subject: 35A02
  topic: subjects
subject: 35B35
  topic: subjects
subject: 35B40
  topic: subjects
creator: Ganesh C. Gorain
creator: Carlos
creator: Octavio Vera
creator: Srikanta Ram
rights: Copyright (c) 2024 Ganesh C. Gorain; Carlos Raposo (Corresponding Author); Octavio Vera, Srikanta Ram https://creativecommons.org/licenses/by/4.0
date: 2024-06-10
publication date: 2024-06-10
starting page: 10
ending page: 21
doi: 10.61383/ejam.20242250

Discrete Multiparameters Potential Boundary Value Problems Involving the \(p(k)\)-Kirchhoff Equations
type: item
description: This paper is concerned with the existence and multiplicity of solutions of discrete inclusions problems involving the so called p(k)-Laplacian operator of Kirchhoff type subjected to potential boundary values conditions.
subject: Research Article
  topic: section
subject: Kirchhoff type equation
  topic: keywords
subject: Potential boundary
  topic: keywords
subject: Discrete inclusion
  topic: keywords
subject: Discrete boundary value problem
  topic: keywords
subject: Critical point theory
  topic: keywords
subject: Variational methods
  topic: keywords
subject: 39A22
  topic: subjects
subject: 39A23
  topic: subjects
subject: 39A27
  topic: subjects
creator: Yassia OUEDRAOGO
creator: Abdoul Aziz Kalifa DIANDA
creator: Blaise KONE
creator: Stanislas OUARO
rights: Copyright (c) 2024 Yassia Ouedraogo, A.A.K. Dianda, Blaise Koné; Stanislas Ouaro (Corresponding Author) https://creativecommons.org/licenses/by/4.0
date: 2024-12-15
publication date: 2024-12-15
starting page: 24
ending page: 41
doi: 10.61383/ejam.20242473

On the Convergence Result for Pseudo-Parabolic Equations with Fractional Time Derivatives
type: item
description: The main goal of this note is to investigate the convergence of solutions of the pseudo-parabolic equation with the Riemann--Liouville derivative when the order tends to \(1^-\). This paper is a continuation of the paper [L.D. Long, D. O'Regan, {Notes on Convergence Results for Parabolic Equations with Riemann-Liouville Derivatives}, Mathematics, 2022] where a special case of the theory below is presented (see Section 1 for a discussion).
subject: Research Article
  topic: section
subject: Fractional diffusion equation
  topic: keywords
subject: Riemman--Liouville
  topic: keywords
subject: convergence rate
  topic: keywords
subject: 35R11
  topic: subjects
subject: 35B65
  topic: subjects
subject: 26A33
  topic: subjects
creator: Donal O'Regan
rights: Copyright (c) 2024 Donal O'Regan https://creativecommons.org/licenses/by/4.0
date: 2024-06-17
publication date: 2024-06-17
starting page: 32
ending page: 38
doi: 10.61383/ejam.20242267

Asymptotic Behavior for 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: Yang Bai
creator: Xiaobin Yao
rights: Copyright (c) 2024 Yang Bai (Corresponding Author); Xiaobin Yao https://creativecommons.org/licenses/by/4.0
date: 2024-09-20
publication date: 2024-09-20
starting page: 63
ending page: 73
doi: 10.61383/ejam.20242378