Journal
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
Volume 43, Issue 1, Pages 25-38Publisher
MALAYSIAN MATHEMATICAL SCIENCES SOC
DOI: 10.1007/s40840-018-0662-5
Keywords
Inverse problems; Time-fractional diffusion equation; Fractional Tikhonov method; Error estimation
Categories
Funding
- Natural Science Foundation of China [11661072]
- Natural Science Foundation of Northwest Normal University, China [NWNU-LKQN-17-5]
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In this paper, we present a new fractional Tikhonov regularization method for solving an inverse problem for a time-fractional diffusion equation which is highly ill-posed in the two-dimensional setting. Fractional Tikhonov regularization method not only retains the advantage of classical Tikhonov method, but also overcomes the effect of over-smoothing of classical Tikhonov method. We give the selection of regularization parameters of the new method and the corresponding error estimation. Furthermore, numerical results show that the fractional Tikhonov method outperforms the classical one.
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