An optimal regularization method for space-fractional backward diffusion problem

In this paper, a space-fractional backward diffusion problem (SFBDP) in a strip is considered. By the Fourier transform, we proposed an optimal modified method to solve this problem in the presence of noisy data. The convergence estimates for the approximate solutions with the regularization parameter selected by an a priori and an a posteriori strategy are provided, respectively. Numerical experiments show that the proposed methods are effective and stable.