Simultaneous inversion of the fractional order and the space-dependent source term for the time-fractional diffusion equation

Zhousheng Ruan, Wen Zhang and Zewen Wang

Applied Mathematics and Computation, 2018, vol. 328, issue C, 365-379

Abstract: In this paper, a simultaneous identification problem of the spacewise source term and the fractional order for a time-fractional diffusion equation is considered. Firstly, under some assumption and with two different kinds of observation data for one-dimensional and two-dimensional time-fractional diffusion equation, the unique results of the inverse problem are proven by the Laplace transformation method and analytic continuation technique. Then the inverse problems are transformed into Tikhonov type optimization problems, the existence of optimal solutions to the Tikhonov functional is proven. Finally, we adopt an alternating minimization algorithm to solve the optimization problems. The efficiency and stability of the inversion algorithm are tested by several one- and two-dimensional examples.

Keywords: Identification of fractional order; Inverse source problem; Uniqueness; Time-fractional diffusion equation (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:328:y:2018:i:c:p:365-379

DOI: 10.1016/j.amc.2018.01.025

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