Regularization methods for solving a time-fractional diffusion inverse source problem

Abstract

This paper studies a time-fractional diffusion ill-posed inverse source problem. We use a simplified Tikhonov regularization method and a Fourier regularization method to solve the problem. Under the selection rules of a priori and a posteriori regularization parameters, a priori and a posteriori error estimates are derived. Among them, the a priori error estimate derived from the simplified Tikhonov regularization method is optimal, while the a posteriori error estimate is quasi-optimal. The a priori and a posteriori error estimates derived by the Fourier regularization method are both optimal. Finally, numerical examples are conducted to demonstrate the effectiveness and stability of the proposed regularization methods.