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Simultaneous determination of a source term and diffusion concentration for a multi-term space-time fractional diffusion equation

    Salman A. Malik   Affiliation
    ; Asim Ilyas   Affiliation
    ; Arifa Samreen   Affiliation

Abstract

An inverse problem of determining a time dependent source term along with diffusion/temperature concentration from a non-local over-specified condition for a space-time fractional diffusion equation is considered. The space-time fractional diffusion equation involve Caputo fractional derivative in space and Hilfer fractional derivatives in time of different orders between 0 and 1. Under certain conditions on the given data we proved that the inverse problem is locally well-posed in the sense of Hadamard. Our method of proof based on eigenfunction expansion for which the eigenfunctions (which are Mittag-Leffler functions) of fractional order spectral problem and its adjoint problem are considered. Several properties of multinomial Mittag-Leffler functions are proved.

Keyword : inverse problem, fractional derivative, Bi-orthogonal system of functions, multinomial Mittag-Leffler function

How to Cite
Malik, S. A., Ilyas, A., & Samreen, A. (2021). Simultaneous determination of a source term and diffusion concentration for a multi-term space-time fractional diffusion equation. Mathematical Modelling and Analysis, 26(3), 411-431. https://doi.org/10.3846/mma.2021.11911
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Jul 13, 2021
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