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

• Published in: Mathematical modelling and analysis Vol. 26; no. 3; pp. 411 - 431
• Main Authors: Malik, Salman A., Ilyas, Asim, Samreen, Arifa
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 13.07.2021
• Subjects: bi-orthogonal system of functions; Diffusion; Eigenvectors; fractional derivative; Functional equations; Functions; inverse problem; Inverse problems; Mathematical research; multinomial mittag-leffler function; Space and time; Spacetime; Time dependence; Pakistan; inverse problem; fractional derivative; Bi-orthogonal system of functions; multinomial Mittag-Leffler function
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2021.11911

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.