Abstract
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.