An inverse problem for fractional diffusion equation in 2-dimensional case: Stability analysis and regularization

In this paper we investigate an inverse problem for a time-fractional diffusion equation which is highly ill-posed in the two-dimensional setting. Based on an a priori assumption, we give a conditional stability result. Some new regularization methods are constructed for solving the inverse problem and the corresponding error estimates are proved. For numerical illustration, several examples are constructed to demonstrate the feasibility and efficiency of the proposed methods.