Filter regularization for an inverse source problem of the time-fractional diffusion equation

In this paper, we focus on a problem of identifying the unknown source of time-fractional diffusion equation. It is known that such problem is ill-posed in the sense that reconstructed solution does not depend continuously on the observation data. Based on this fact, a GFR (general filter regularized method) is proposed. We further give the error convergence estimates under deterministic case and random noise, respectively. Lastly, some special cases and numerical examples are presented to illustrate the efficiency of our method.