Abstract. We construct a generalized mathematical model to describe the fractional differential dynamics of filtration processes in fractured porous media, based on the use of the concept of Hilfer–Prabhakar fractional derivative. Within the framework of this model, we obtain a number of closed solutions to boundary-value problems of filtration theory for modeling the dynamics of pressures at launch of wells in case of plane-radial filtration, as well as by activity of galleries under plane-parallel filtration.

Keywords: mathematical modeling, fractional-differential dynamics of filtration processes, fractured porous media, non-classical models, equation of filtration with Hilfer–Prabhakar fractional derivative, boundary value problems, closed form solutions.