Regularization of inverse source problem for fractional diffusion equation with Riemann–Liouville derivative

Abstract

In this paper, we consider an inverse source problem for fractional diffusion equation with Riemann–Liouville derivative. The considered problem is ill-posed, i.e., the solution does not depend continuously on the given data. We assume the solutions of the equation can be represented by a Fourier series. The Tikhonov regularization method is applied to solve this problem. In the theoretical results, the convergence estimates between the exact solutions and the regularized solutions are presented under a priori and a posteriori parameter choice rules.