Simultaneous inversion of the potential term and the fractional orders in a multi-term time-fractional diffusion equation

In the present paper, we devote our effort to a nonlinear inverse problem for simultaneously recovering the potential function and the fractional orders in a multi-term time-fractional diffusion equation from the noisy boundary Cauchy data in the one-dimensional case. The uniqueness for the inverse...

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Bibliographic Details
Published in:Inverse problems 2021-05, Vol.37 (5), p.55007
Main Authors: Sun, L L, Li, Y S, Zhang, Y
Format: Article
Language:English
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Summary:In the present paper, we devote our effort to a nonlinear inverse problem for simultaneously recovering the potential function and the fractional orders in a multi-term time-fractional diffusion equation from the noisy boundary Cauchy data in the one-dimensional case. The uniqueness for the inverse problem is derived based on the analytic continuation, the Laplace transformation and the Gel’fand–Levitan theory. Finally, the Levenberg–Marquardt regularization method with a regularization parameter chosen by a sigmoid-type function is applied for finding a stable approximate solution. Three numerical examples are provided to show the effectiveness of the proposed method.
ISSN:0266-5611
1361-6420
DOI:10.1088/1361-6420/abf162