Open AccessON BOUNDARY VALUE PROBLEM FOR GENERALIZED ALLER EQUATION
Author(s) -
С Х Геккиева,
M. M. Karmokov,
Марат Асланбиевич Керефов
Publication year - 2021
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2020-26-2-7-14
Subject(s) - mathematics , fractional calculus , fractal , porous medium , boundary value problem , differential equation , mathematical analysis , porosity , materials science , composite material
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 withRiemann 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.