Approximate Solutions of Inverse Problems for Nonlinear Space Fractional Diffusion Equations with Randomly Perturbed Data

This paper is concerned with the backward problem for nonlinear space fractional diffusion with additive noise on the right-hand side and the final value. To regularize the unstable solution, we develop a new regularized method for solving the problem. In the case of constant coefficients, we use the truncation methods. In the case of perturbed time dependent coefficients, we apply a new quasi-reversibility method. We also show the convergence rate between the regularized solution and the sought solution under some a priori assumption on the sought solution.