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Mathematical Modeling of Fractional Differential Filtration Dynamics Based on Models with Hilfer–Prabhakar Derivative

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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 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.

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    V. M. Bulavatsky

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  1. V. M. Bulavatsky
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Correspondence to V. M. Bulavatsky.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 2, March–April, 2017, pp. 51–64.

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Bulavatsky, V.M. Mathematical Modeling of Fractional Differential Filtration Dynamics Based on Models with Hilfer–Prabhakar Derivative. Cybern Syst Anal 53, 204–216 (2017). https://doi.org/10.1007/s10559-017-9920-z

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