Fractional Landweber Iterative Regularization Method for Identifying the Unknown Source of the Time-Fractional Diffusion Problem

In this paper, we study an inverse problem to determine an unknown source term in the time-fractional diffusion equation with variable coefficients in a general bound domain. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. We introduce the fractional Landweber iterative regularization method to solve inverse source problem. Based on an a conditional stability result, error convergent estimates between the exact solution and the regularization solution by using an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule are also given. Some numerical experiments prove that the fractional Landweber method provides better numerical result than the classical Landweber method under the same iterative steps.