Bulavatsky V.M.
Mathematical modeling of fractional differential filtration dynamics based on models with Hilfer–Prabhakar derivative

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 form 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. © 2017, Springer Science+Business Media New York.

Keywords: boundary-value problems, closed form solutions, equation of filtration with Hilfer–Prabhakar fractional derivative, fractional differential dynamics of filtration processes, fractured porous media, mathematical modeling, non-classical models, Boundary value problems, Dynamics, Filtration, Mathematical models, Classical model, Closed form solutions, Filtration process, Fractional derivatives, Fractured porous media, Porous materials

Cite:
Bulavatsky V.M. (2017). Mathematical modeling of fractional differential filtration dynamics based on models with Hilfer–Prabhakar derivative. Cybernetics and Systems Analysis, 53 (2), 51-64. doi: https://doi.org/10.1007/s10559-017-9920-z http://jnas.nbuv.gov.ua/article/UJRN-0000670410 [In Russian].