Inverse source problems for multi-parameter space-time fractional differential equations with bi-fractional Laplacian operators

M. J. Huntul; M. J. Huntul

doi:10.3934/math.20241566

AIMS Mathematics

2024, Volume 9, Issue 11: 32734-32756. doi: 10.3934/math.20241566

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Research article

Inverse source problems for multi-parameter space-time fractional differential equations with bi-fractional Laplacian operators

M. J. Huntul ^,

Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Saudi Arabia

Received: 31 August 2024 Revised: 21 October 2024 Accepted: 25 October 2024 Published: 19 November 2024
MSC : 35R30, 35K10, 35A09, 35A01, 35A02

Two inverse source problems for a space-time fractional differential equation involving bi-fractional Laplacian operators in the spatial variable and Caputo time-fractional derivatives of different orders between 1 and 2 are studied. In the first inverse source problem, the space-dependent term along with the diffusion concentration is recovered, while in the second inverse source problem, the time-dependent term along with the diffusion concentration is identified. Both inverse source problems are ill-posed in the sense of Hadamard. The existence and uniqueness of solutions for both inverse source problems are investigated. Finally, several examples are presented to illustrate the obtained results for the inverse source problems.
- inverse source problem,
- fractional derivative,
- bi-fractional Laplacian operator,
- Ill-posedness,
- Mittag-Leffler type functions
Citation: M. J. Huntul. Inverse source problems for multi-parameter space-time fractional differential equations with bi-fractional Laplacian operators[J]. AIMS Mathematics, 2024, 9(11): 32734-32756. doi: 10.3934/math.20241566

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Abstract

Two inverse source problems for a space-time fractional differential equation involving bi-fractional Laplacian operators in the spatial variable and Caputo time-fractional derivatives of different orders between 1 and 2 are studied. In the first inverse source problem, the space-dependent term along with the diffusion concentration is recovered, while in the second inverse source problem, the time-dependent term along with the diffusion concentration is identified. Both inverse source problems are ill-posed in the sense of Hadamard. The existence and uniqueness of solutions for both inverse source problems are investigated. Finally, several examples are presented to illustrate the obtained results for the inverse source problems.

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