An a posteriori Fourier regularization method for identifying the unknown source of the space-fractional diffusion equation

In this paper, we identify the unknown source which depends only on spatial variable for a fractional diffusion equation using the Fourier method. Not alike the previous literature, we propose to choose the regularization parameter by an a posteriori rule, with which we can obtain error estimate of Hölder type between the exact solution and the regularized approximation. Numerical simulations show that the proposed scheme is effective and stable. MSC: 35R30, 47A52, 65M30, 65M32.