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

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.

Keywords

• inverse source problem
• fractional derivative
• bi-fractional laplacian operator
• ill-posedness
• mittag-leffler type functions