Regularization of a terminal value problem for time fractional diffusion equation

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 res...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 43; no. 6; pp. 3850 - 3878
Main Authors Anh Triet, Nguyen, Van Au, Vo, Dinh Long, Le, Baleanu, Dumitru, Huy Tuan, Nguyen
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 01.04.2020
Subjects
fractional diffusion equation
inverse problem
Inverse problems
Regularization
Regularization methods
Riemann‐Lioville fractional derivative
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6159