An Inverse Source Problem for A One-dimensional Time-Space Fractional Diffusion Equation

Abstract

For the fractional diffusion equation, it has received extensive study from various angles on the inverse problem. This paper is dedicated to determining a source term with time-dependence of the time-space fractional diffusion equation with additional observation data. First, the implicit difference scheme and the matrix transfer technique are used to solve an initial boundary value direct problem, in which the time-space fractional diffusion equation for the homogeneous Dirichlet boundary condition is considered. For the conclusive solution of the given inverse source problem, a numerical method is proposed based on the optimal perturbation algorithm with optimized Tikhonov regularization. The numerical examples illustrate that our proposed numerical method is highly effective and relatively stable.