The method of fundamental solution for the inverse source problem for the space-fractional diffusion equation

In this article, a meshless numerical method for solving the inverse source problem of the space-fractional diffusion equation is proposed. The numerical solution is approximated using the fundamental solution of the space-fractional diffusion equation as a basis function. Since the resulting matrix equation is extremely ill-conditioned, a regularized solution is obtained by adopting the Tikhonov regularization scheme, in which the choice of the regularization parameter is based on generalized cross-validation criterion. Two typical numerical examples are given to verify the efficiency and accuracy of the proposed method.