A Riesz-Feller space-fractional backward diffusion problem with a time-dependent coefficient: regularization and error estimates

In this paper, we consider a Riesz-Feller space-fractional backward diffusion problem with a time-dependent coefficient u(x,t)+f(x,t),(x,t)Rx(0,T). We show that this problem is ill-posed; therefore, we propose a convolution regularization method to solve it. New error estimates for the regularized solution are given under a priori and a posteriori parameter choice rules, respectively. Copyright (c) 2016 John Wiley & Sons, Ltd.