Identifying the space source term problem for time-space-fractional diffusion equation

Abstract

Abstract In this paper, we consider an inverse source problem for the time-space-fractional diffusion equation. Here, in the sense of Hadamard, we prove that the problem is severely ill-posed. By applying the quasi-reversibility regularization method, we propose by this method to solve the problem (1.1). After that, we give an error estimate between the sought solution and regularized solution under a prior parameter choice rule and a posterior parameter choice rule, respectively. Finally, we present a numerical example to find that the proposed method works well.

Keywords

• Inverse source problem
• Time-space-fractional diffusion equation
• Ill-posed problem
• Convergence estimates
• Regularization method