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Regularization of a terminal value problem for time fractional diffusion equation
Author(s) -
Anh Triet Nguyen,
Van Au Vo,
Dinh Long Le,
Baleanu Dumitru,
Huy Tuan Nguyen
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6159
Subject(s) - mathematics , regularization (linguistics) , hadamard transform , a priori and a posteriori , inverse problem , well posed problem , boundary value problem , diffusion equation , mathematical analysis , mathematical optimization , computer science , philosophy , economy , epistemology , artificial intelligence , economics , service (business)
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.