Regularization of a terminal value problem for time fractional diffusion equation

Authors: Nguyễn Anh Triết, Nguyễn Huy Tuấn, Dumitru Baleanu, Le Dinh Long, Võ Văn Âu, Nguyễn Huy Tuấn,

https://doi.org/10.1002/mma.6159

Publisher, magazine: ,

Publication year: 2020

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Abstract

In this article, we study an inverse problem with inhomogeneous source to determine an initial data from the time fractional diffusion equation. In general, this problem is ill‐posed in the sense of Hadamard, so the quasi‐boundary value method is proposed to solve the problem. In the theoretical results, we propose a priori and a posteriori parameter choice rules and analyze them. Finally, two numerical results in the one‐dimensional and two‐dimensional case show the evidence of the used regularization method.

Tags: fractional diffusion equation, inverse problem, regularization, Riemann-Lioville fractionalderivative