Numerical algorithms for solving the anomalous diffusion inverse problems

The anomalous diffusion process in a layered medium is considered. The boundary problem for the differential equation in fractional derivations is formulated. The difference approximation of the boundary problem with the Grunewald-Letnikov fractional derivative as the difference counterpart for the Riemann-Liouville fractional derivative is used. The inverse problems consist in restoration of the layered medium key parameters including the anomalous diffusion index that describes its complexity. The numerical algorithms based on the difference scheme inversion method are discussed. The results of numerical simulations are presented and their comparative analysis is provided.