Simultaneous inversion for a fractional order and a time source term in a time-fractional diffusion-wave equation

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS(2023)

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摘要
In this article, we consider an inverse problem for determining simultaneously a fractional order and a time-dependent source term in a multi-dimensional time-fractional diffusion-wave equation by a nonlocal condition. Based on a uniformly bounded estimate of the Mittag-Leffler function given in this paper, we prove the uniqueness of the inverse problem and the Lipschitz continuity properties for the direct problem. Then we employ the Levenberg-Marquardt method to recover simultaneously the fractional order and the time source term, and establish a finite-dimensional approximation algorithm to find a regularized numerical solution. Moreover, a fast tensor method for solving the direct problem in the three-dimensional case is provided. Some numerical results in one and multidimensional spaces are presented for showing the robustness of the proposed algorithm.
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关键词
fractional order,simultaneous inversion,time source term,time-fractional,diffusion-wave
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