Some Boundary-Value Problems Corresponding to the Model of Fractional Differential Filtration Dynamics in a Fractured Porous Media Under the Condition of Time Non-Locality

Closed-form solutions to some boundary-value problems of fractional differential geofiltration dynamics in a fractured porous medium are obtained for a model with weakly permeable porous blocks. In particular, the direct and inverse boundary-value problems of filtration for the finite thickness layer are solved, the conditions for the existence of their regular solutions are given, and a solution to the problem of filtration dynamics with nonlocal boundary conditions is found. For a particular case of the filtration model, the problem of modeling the anomalous dynamics of filtration pressure fields on a star-shaped graph is considered.