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

  • Kaifang Liao , Lei Zhang and Ting Wei ORCID logo EMAIL logo
Published/Copyright: September 21, 2023

Abstract

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.

MSC 2010: 65M32; 35R11

Award Identifier / Grant number: 12171215

Award Identifier / Grant number: U1804158

Award Identifier / Grant number: 22JR5RA391

Funding statement: This paper was supported by the NSF of China (12171215), NSF of Gansu (22JR5RA391) and NSF of China (U1804158).

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Received: 2020-05-18
Revised: 2023-03-20
Accepted: 2023-04-29
Published Online: 2023-09-21
Published in Print: 2023-10-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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