Some Modeling Problems of Fractional-Differential Geofiltrational Dynamics within the Framework of Generalized Mathematical Models

摘要

The generalized mathematical models depicting fractional-differential dynamics of filtration processes in complex geoporous structures under nonequilibrium conditions are introduced. The construction of corresponding fractional-differential mathematical models is based on generalization of Darcy filtration law using the concept of biordinal fractional Hilfer derivative on time variable that allows one to reach a large degree of generality of models studied. Within the framework of considered nonclassical mathematical models some nonstationary boundary value problems of the theory of nonequilibrium geofiltration are formulated and their analytical solutions are obtained.