Determination of Sub-Diffusion Process and Source Term from Nonlocal Data: Applications to Microwave Radiations

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DOI: https://doi.org/10.28924/2291-8639-23-2025-218
Published: Sep 8, 2025
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Ilyas Khan, Arifa Samreen, Saqib Zia, Ansar Javed, Wei Sin Koh, Determination of Sub-Diffusion Process and Source Term from Nonlocal Data: Applications to Microwave Radiations, Int. J. Anal. Appl., 23 (2025), 218.

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Ilyas Khan, Arifa Samreen, Saqib Zia, Ansar Javed, Wei Sin Koh

Abstract

We investigate two inverse problems (IPs) for the time fractional diffusion equation (TFDE) with an involution. The determination of a space varying source term, along with solution of a diffusion equation containing n fractional order derivatives in Caputo’s sense from extra data at a specific time, constitutes the first IP. The second IP investigates the extracting of a time varying source term as well as the solution of the TFDE from non-local type extra condition. The second IP has applications to microwave radiations. The existence and uniqueness results for the solutions of both IPs are presented.

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