Solving the backward problem for space-fractional diffusion equation by a fractional Tikhonov regularization method

In this paper, we consider the backward problem for diffusion equation with space-fractional Laplacian. In order to overcome the ill-posedness of the backward problem, we propose a fractional Tikhonov regularization method to solve it. Based on the conditional stability estimate and an a posteriori regularization parameter choice rule, the convergence rate estimate is presented under a-priori bound assumption for the exact solution. Finally, several numerical examples are given to show that the proposed numerical methods are effective.