Recovering Source Term and Temperature Distribution for Nonlocal Heat Equation

Asim Ilyas, Salman A. Malik and Summaya Saif

Applied Mathematics and Computation, 2023, vol. 439, issue C

Abstract: We consider two problems of recovering the source terms along with heat concentration for a time fractional heat equation involving the so-called mth level fractional derivative (LFD) (proposed in a paper by Luchko [1]) in time variable of order between 0 and 1. The solutions of both problems are obtained by using eigenfunction expansion method. The series solutions of the inverse problems are proved to be unique and regular. The ill-posedness of inverse problems is proved in the sense of Hadamard and some numerical examples are presented.

Keywords: Inverse problem; Generalized fractional derivative; Riesz basis; Mittag-Leffler functions (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:439:y:2023:i:c:s009630032200683x

DOI: 10.1016/j.amc.2022.127610

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