Boundary-Value Problems for Space-Time Fractional Differential Filtration Dynamics in Fractured-Porous Media

Closed-form solutions are obtained for some non-stationary boundary-value problems of filtration dynamics in fractured-porous formations, posed within the framework of fractional-differential mathematical models, taking into account the space-time nonlocality of the process. The mathematical models of anomalous filtration dynamics are formulated using the Hilfer or Caputo derivatives with respect to the time variable and the Riemann–Liouville derivative with respect to the geometric variable. Along with direct filtration problems, the authors also consider the inverse boundary-value problem of determining the unknown source function that depends only on the geometric variable. Conditions of the existence of regular solutions to the considered problems are given.