Journal
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
Volume 28, Issue 2, Pages 211-235Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/jiip-2018-0040
Keywords
Ill-posed; regularization method; Caputo's fractional derivatives; Fourier transform
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Funding
- Vietnam National Foundation for Science and Technology Development (NAFOSTED) [101.02-2019.09]
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In this paper, we consider an inverse problem for a time-fractional diffusion equation with a nonlinear source. We prove that the considered problem is ill-posed, i.e., the solution does not depend continuously on the data. The problem is ill-posed in the sense of Hadamard. Under some weak a priori assumptions on the sought solution, we propose a new regularization method for stabilizing the ill-posed problem. We also provide a numerical example to illustrate our results.
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