On a backward problem for nonlinear fractional diffusion equations

In this paper, a backward problem for a time-space fractional diffusion with nonlinear source has been considered. Under some assumptions, we establish the existence and uniqueness of mild solutions of a local solution to the nonlinear problem. We also prove that our backward problem is ill-posed in the sense of Hadamard. A regularization method has been proposed to approximate the solution. Furthermore, the convergence rate for the regularized solution can be proved. (C) 2018 Elsevier Ltd. All rights reserved.