A regularization for a Riesz–Feller space-fractional backward diffusion problem

Abstract

In the present paper, we consider a space-fractional backward diffusion problem, where data is given at t = T and the solution is required in the interval 0 < t < T. However, it is an ill-posed problem since the solution does not depend continuously on the data. Here, we give a new iteration regularization method to deal with this problem, and error estimates are obtained for a priori and a posteriori parameter choice rules, respectively. Furthermore, numerical implement shows the proposed method works effectively.