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 Vestnik SamU. Estestvenno-Nauchnaya Ser., 2020, Volume 26, Issue 2, Pages 7–14 (Mi vsgu626)

Mathematics

On boundary value problem for generalized Aller equation

S.Kh. Gekkievaa, M. M. Karmokovb, M. A. Kerefovb

a Kabardin-Balkar Scientific Center of the Russian Academy of Sciences, Nalchik, Russian Federation
b Kabardino-Balkarian State University named after H.M. Berbekov, Nalchik, Russian Federation

Abstract: The mathematical models of fluid filtration processes in porous media with a fractal structure and memory are based on differential equations of fractional order in both time and space variables. The dependence of the soil water content can significantly affect the moisture transport in capillary-porous media. The paper investigates the generalized Aller equation widely used in mathematical modeling of the processes related to water table dynamics in view of fractal structure. As a mathematical model of the Aller equation with Riemann–Liouville fractional derivatives, a loaded fractional order equation is proposed, and a solution to the Goursat problem has been written out for this model in explicit form.

Keywords: Aller equation, Goursat problem, Riemann–Liouville fractional integrodifferential operator, moisture transfer equation, generalized Newton–Leibniz formula, loaded equation, Volterra equation of the second kind, Laplace convolution.

DOI: https://doi.org/10.18287/2541-7525-2020-26-2-7-14

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UDC: 517.95
Revised: 18.03.2020
Accepted:25.05.2020

Citation: S.Kh. Gekkieva, M. M. Karmokov, M. A. Kerefov, “On boundary value problem for generalized Aller equation”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 26:2 (2020), 7–14

Citation in format AMSBIB
\Bibitem{GekKarKer20} \by S.Kh.~Gekkieva, M.~M.~Karmokov, M.~A.~Kerefov \paper On boundary value problem for generalized Aller equation \jour Vestnik SamU. Estestvenno-Nauchnaya Ser. \yr 2020 \vol 26 \issue 2 \pages 7--14 \mathnet{http://mi.mathnet.ru/vsgu626} \crossref{https://doi.org/10.18287/2541-7525-2020-26-2-7-14} \elib{https://elibrary.ru/item.asp?id=44613893}