Two Regularization Methods for an Unknown Source Problem for the Tempered Fractional Diffusion Equation

Abstract

In this work, we focus on the inverse source problem for tempered fractional diffusion equation. The problem is ill-posed. We introduce a modified quasi boundary method and the fractional Landweber method to tackle this issue. In the convergence results, we present the errors under two choices: the a priori and the a posteriori strategies. Finally, we provide numerical example to demonstrate the efficacy and stability of the proposed methodologies.