Stable numerical solution of an inverse coefficient problem for a time fractional reaction-diffusion equation‎

In this paper, an inverse problem of determining an unknown reaction coefficient in a one-dimensional time-fractional reaction-diffusion equation is considered. This inverse problem is generally ill-posed. For this reason, the mollification regularization technique with the generalized cross-validation criteria will be employed to find an equivalent stable problem. Afterward, a finite difference marching scheme is introduced to solve this regularized problem. The stability and convergence of the numerical solution are investigated. In the end, some numerical examples are presented to verify the ability and effectiveness of the proposed algorithm.