An inverse space-dependent source problem for a multi-term time fractional diffusion equation

In the present paper, we consider an inverse problem of recovering the space-dependent source for a multi-term time fractional diffusion equation from noisy final data. First, we proved that the direct problem has a unique solution. Second, we proved the existence and uniqueness for the inverse space-dependent source problem. We also prove the ill-posedness of the inverse problem by compactness of input-output mapping. Then, we use a non-stationary iterative Tikhonov regularization method combined with a finite dimensional approximation to find a stable source. Four different examples are presented to show the feasibility and efficiency of the proposed method.