Recovering solution of the Reverse nonlinear time Fractional diffusion equations with fluctuations data

Authors

https://doi.org/10.61383/ejam.20231237

Keywords:

Riemann-Liouville, Regularized solution, Gaussian white noise, Ill-posed

Abstract

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.

References

Nguyen Huy Tuan, Nguyen Hoang Tuan, Dumitru Baleanu, and Tran Ngoc Thach, On a backward problem for fractional diffusion equation with riemann-liouville derivative, Mathematical Methods in the Applied Sciences 43 (2019), no. 3, 1292–1312. DOI: https://doi.org/10.1002/mma.5943

Nguyen Anh Triet, Tran Thanh Binh, Nguyen Duc Phuong, Dumitru Baleanu, and Nguyen Huu Can, Recovering the initial value for a system of nonlocal diffusion equations with random noise on the measurements, Mathematical Methods in the Applied Sciences 44 (2020), no. 6, 5188–5209. DOI: https://doi.org/10.1002/mma.7102

Tran Bao Ngoc, Yong Zhou, Donal O’Regan, and Nguyen Huy Tuan, On a terminal value problem for pseudo parabolic equations involving riemann–liouville fractional derivatives, Applied Mathematics Letters 106 (2020), 106373. DOI: https://doi.org/10.1016/j.aml.2020.106373

Nguyen Duc Phuong, Dumitru Baleanu, Tran Thanh Phong, and Le Dinh Long, Recovering the source term for parabolic equation with nonlocal integral condition, Mathematical Methods in the Applied Sciences 44 (2021), no. 11, 9026–9041. DOI: https://doi.org/10.1002/mma.7331

Nguyen Duc Phuong, Tran Binh, and Nguyen Luc, On a final value problem for parabolic equation on the sphere with linear and nonlinear source, Advances in the Theory of Nonlinear Analysis and its Application 4 (2020), no. 3, 143–151. DOI: https://doi.org/10.31197/atnaa.753458

Igor Podlubny, Fractional differential equations, Academic Press, New York, 1999.

Guang An Zou and Bo Wang, Stochastic burgers’ equation with fractional derivative driven by multiplicative noise, Computers & Mathematics with Applications 74 (2017), no. 12, 3195–3208. DOI: https://doi.org/10.1016/j.camwa.2017.08.023

Nguyen Duc Phuong, Nguyen Huy Tuan, Zakia Hammouch, and Rathinasamy Sakthivel, On a pseudo-parabolic equations with a non-local term of the kirchhoff type with random gaussian white noise, Chaos, Solitons and Fractals 145 (2021), 110771. DOI: https://doi.org/10.1016/j.chaos.2021.110771

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Published

2023 Sep 09

How to Cite

[1]
T. X. Doan Thi and T. H. Vo Thi, “Recovering solution of the Reverse nonlinear time Fractional diffusion equations with fluctuations data”, Electron. J. Appl. Math., vol. 1, no. 2, pp. 60–70, Sep. 2023.

Issue

Vol. 1 No. 2 (2023)

Section

Research Article

License

Copyright (c) 2023 Doan Thi Thanh Xuan; Vo Thi Thanh Ha (Corresponding Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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.
 
 
Received 2023 Aug 02
Accepted 2023 Sep 05
Published 2023 Sep 09