TIKHONOV REGULARIZATION METHOD OF AN INVERSE SPACE-DEPENDENT SOURCE PROBLEM FOR A TIME-SPACE FRACTIONAL DIFFUSION EQUATION

The aim of this paper is to identify a space-dependent source term in the time-space fractional diffusion equation with an initial-boundary data and an additional measurement data at the final time point. A series expression for the solution of the direct problem is used to transfer the inverse problem into the first type of Fredholm integral equation. Before solving the inverse problem, the uniqueness of its solution is proved. We then use the Tikhonov regularization method to deal with the integral equation and obtain a series expression for the regularized solution of the inverse problem. Moreover, according to the prior and the posterior regularization parameter selection rules, we prove the convergence rates of the regularization solution. Finally, we provide some numerical experiments to show the effectiveness of our method.