An inverse problem for space-fractional backward diffusion problem

In this paper, an inverse problem for space-fractional backward diffusion equation, which is highly ill-posed, is considered. This problem is obtained from the classical diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha is an element of (0,2]. We show that such a problem is severely ill-posed, and further present a simplified Tikhonov regularization method to deal with this problem. Convergence estimate is presented under a priori choice of regularization parameter. Numerical experiments are given to illustrate the accuracy and efficiency of the proposed method. Copyright (c) 2013 John Wiley & Sons, Ltd.