Abstract

In this paper, we study a backward problem for a fractional diffusion equationwith nonlinear source in a bounded domain. By applying the properties ofMittag-Leffler functions and Banach fixed point theorem, we establish someresults above the existence, uniqueness, and regularity of the mild solutionsof the proposed problem in some suitable space. Moreover, we also showthe ill-posedness of our problem in the sense of Hadamard. The regularizedsolution is given, and the convergence rate between the regularized solution andthe exact solution is also obtained