  This paper is concerned with backward problem for nonlinear space fractional
diffusion with additive noise on the right-hand side and the final value. To
regularize the instable solution, we develop some 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.
