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Research Article | Open Access

Inverse source problem for multi-term time-fractional diffusion equation with nonlocal boundary conditions

Bauyrzhan Derbissaly( ), Makhmud Sadybekov
Institute of Mathematics and Mathematical Modeling, 125 Pushkin Street, Almaty, 050010, Kazakhstan
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Abstract

In this paper, we consider an inverse source problem with nonlocal boundary conditions for the heat equation involving multi-term time-fractional derivatives. We determine a source term independent of the space variable, and the temperature distribution from the energy measurement. We reduce the solution of the inverse problem to finding solutions to two problems. The well-posedness of each problem is shown using the generalized Fourier method.

Keywords

inverse source problemfractional diffusion equationnonlocal boundary conditionmultinomial Mittag-Lefler functionFourier series
CLC number: 35A09, 26A33, 45J05, 34K37, 42A16

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AIMS Mathematics
Volume 9 Issue 4,
April 2024
Pages 9969-9988
DOI: 10.3934/math.2024488

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Cite this article:
Derbissaly B, Sadybekov M. Inverse source problem for multi-term time-fractional diffusion equation with nonlocal boundary conditions. AIMS Mathematics, 2024, 9(4): 9969-9988. https://doi.org/10.3934/math.2024488

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Received: 31 January 2024
Revised: 21 February 2024
Accepted: 01 March 2024
Published: 15 April 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)