Final value problem for nonlinear time fractional reaction-diffusion equation with discrete data

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:376

Article

Nguyen Huy Tuan¹  Baleanu, Dumitru^2,3,4  Tran Ngoc Thach^5,6  O'Regan, Donal⁷  Nguyen Huu Can⁸ 

[1] Duy Tan Univ, Inst Res & Dev, Da Nang 550000, Vietnam

[2] Cankaya Univ, Dept Math, Ankara, Turkey

[3] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung, Taiwan

[4] Inst Space Sci, Magurele, Romania

[5] Univ Sci, Dept Math & Comp Sci, Ho Chi Minh City, Vietnam

[6] Vietnam Natl Univ, Ho Chi Minh City, Vietnam

[7] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland

[8] Ton Duc Thang Univ, Fac Math & Stat, Appl Anal Res Grp, Ho Chi Minh City, Vietnam

关键词: Backward problem;    Fractional reaction-diffusion equation;    Regularization method;    Nonlinear source;    Discrete data;   

DOI  :  10.1016/j.cam.2020.112883

来源: Elsevier

【 摘 要 】

In this paper, we study the problem of finding the solution of a multi-dimensional time fractional reaction-diffusion equation with nonlinear source from the final value data. We prove that the present problem is not well-posed. Then regularized problems are constructed using the truncated expansion method (in the case of two-dimensional) and the quasi-boundary value method (in the case of multi-dimensional). Finally, convergence rates of the regularized solutions are given and investigated numerically. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

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