A Modified Iteration Method for an Inverse Problem of Diffusion Equation with Laplace and Riesz-Feller Space Fractional Operators

We investigate a backward problem in time of diffusion equation with Laplace and Riesz-Feller space fractional operators. Firstly, inspired by the classical Landweber iterative method, a modified iterative regularization method is proposed to restore the continuous dependence of solution on the measurement data, and then under the a-priori and a-posteriori selection rules of regularization parameter, we give and prove the convergence estimations of regularization solution. Finally, we verify the regularization effect of modified iterative method by doing some numerical experiments. Numerical results show that this method is stable and feasible when it is used to deal with the inverse problem in this article.