Some Boundary-Value Problems of Fractional Differential Filtration Dynamics Regarding the Biparabolic Mathematical Model

Closed-form solutions are obtained to some one-dimensional boundary-value problems of modeling anomalous filtration dynamics in a layered geoporous medium, posed within the framework of the fractional differential generalization of the biparabolic evolutionary fourth-order partial differential equation. In particular, the statements and solutions to the direct and inverse model boundary-value problems of geofiltration dynamics based on the mathematical model with conjugation conditions are presented, and the existence conditions for the regular solutions to these problems are determined.