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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/vsgu626
https://www.mathnet.ru/eng/vsgu/v26/i2/p7
This publication is cited in the following 2 articles:
M. A. Kerefov, S. Kh. Gekkieva, B. M. Kerefov, “Pervaya kraevaya zadacha dlya uravneniya Allera—Lykova s drobnoi proizvodnoi Kaputo”, Materialy Mezhdunarodnoi konferentsii «Klassicheskaya i sovremennaya geometriya», posvyaschennoi 100-letiyu so dnya rozhdeniya professora Levona Sergeevicha Atanasyana (15 iyulya 1921 g.—5 iyulya 1998 g.). Moskva, 1–4 noyabrya 2021 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 221, VINITI RAN, M., 2023, 63–70
Yury Kostikov, Aleksandr Romanenkov, “On solution of pseudohyperbolic equation with constant coefficients”, RDLUZ, 14:39 (2023), 225
Citation in format AMSBIB
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