QUASIREVERSIBILITY METHOD FOR THE ONE-DIMENSIONAL BACKWARD TIME-SPACE FRACTIONAL DIFFUSION PROBLEM

A backward problem for one-dimensional time-space fractional diffusion process is considered. That is to determine the initial data from a noisy final data. In general, the inverse problem is ill-posed and the quasireversibility regularization method is used to solve it. Based on a priori and a posteriori regularization parameter selection rules, the corresponding convergence error estimates of the proposed regularization method are obtained, respectively. Finally, several numerical examples are presented to verify that our proposed scheme works well.