An inverse source Cauchy-weighted time-fractional diffusion problem

Year 2024, Volume: 53 Issue: 5, 1354 - 1367, 15.10.2024

Rahima Atmania , Loubna Settara

https://doi.org/10.15672/hujms.1230169

Abstract

In the present paper, we are concerned with an inverse source Cauchy weighted problem involving a one-dimensional diffusion equation with a time-fractional Riemann-Liouville derivative with $0<\alpha <1$. We start with results on the existence and regularity of the weak solution of the direct problem. Then, we investigate the invertibility of the input-output mapping defined by the additional over-determination integral data in order to the determination of the unknown time-dependent source coefficient.

Keywords

inverse source problem, time-fractional diffusion equation, Riemann-Liouville fractional derivative, Cauchy-weighted problem, input-output mapping

Supporting Institution

LMA, Laboratory of applied mathemtics

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