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

Bauyrzhan Derbissaly; Makhmud Sadybekov; Bauyrzhan Derbissaly; Makhmud Sadybekov

doi:10.3934/math.2024488

AIMS Mathematics

2024, Volume 9, Issue 4: 9969-9988. doi: 10.3934/math.2024488

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Research article

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

Institute of Mathematics and Mathematical Modeling, 125 Pushkin Street, Almaty, 050010, Kazakhstan

Received: 31 January 2024 Revised: 21 February 2024 Accepted: 01 March 2024 Published: 12 March 2024
MSC : 35A09, 26A33, 45J05, 34K37, 42A16

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.
- inverse source problem,
- fractional diffusion equation,
- nonlocal boundary condition,
- multinomial Mittag-Lefler function,
- Fourier series
Citation: Bauyrzhan Derbissaly, Makhmud Sadybekov. Inverse source problem for multi-term time-fractional diffusion equation with nonlocal boundary conditions[J]. AIMS Mathematics, 2024, 9(4): 9969-9988. doi: 10.3934/math.2024488

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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.

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