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. (C) 2017 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.