Fractional Tikhonov Regularization Method for a Time-Fractional Backward Heat Equation with a Fractional Laplacian

Jianlin Wang; Xiangtuan Xiong; Xiaoxiao Cao

doi:10.4208/jpde.v31.n4.4

Fractional Tikhonov Regularization Method for a Time-Fractional Backward Heat Equation with a Fractional Laplacian

Authors

Jianlin Wang Department of Mathematics, Renmin University of China, Beijing 100872, China.
Xiangtuan Xiong Department of Mathematics, Northwest Normal University, Lanzhou 730000, P.R. China.
Xiaoxiao Cao Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

DOI:

https://doi.org/10.4208/jpde.v31.n4.4

Keywords:

Inverse problem;Ill-posedness;error estimate;fractional regularization method.

Abstract

In this paper, we consider a time-fractional backward problem with a fractional Laplacian. We propose a fractional Tikhonov regularization method for solving this problem under the the a-priori parameter choice rule. Error estimates are proved. Some numerical examples are shown to verify the effectiveness of the proposed method.

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Published

2020-05-12

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Issue

Vol. 31 No. 4 (2018)

Section

Articles

How to Cite

Fractional Tikhonov Regularization Method for a Time-Fractional Backward Heat Equation with a Fractional Laplacian. (2020). Journal of Partial Differential Equations, 31(4), 333-342. https://doi.org/10.4208/jpde.v31.n4.4