Numerical Method for the Variable-Order Fractional Filtration Equation in Heterogeneous Media
Alimbekova N. Bakishev A. Berdyshev A.
November 2024Multidisciplinary Digital Publishing Institute (MDPI)
Fractal and Fractional
2024#8Issue 11
This paper presents a study of the application of the finite element method for solving a fractional differential filtration problem in heterogeneous fractured porous media with variable orders of fractional derivatives. A numerical method for the initial-boundary value problem was constructed, and a theoretical study of the stability and convergence of the method was carried out using the method of a priori estimates. The results were confirmed through a comparative analysis of the empirical and theoretical orders of convergence based on computational experiments. Furthermore, we analyzed the effect of variable-order functions of fractional derivatives on the process of fluid flow in a heterogeneous medium, presenting new practical results in the field of modeling the fluid flow in complex media. This work is an important contribution to the numerical modeling of filtration in porous media with variable orders of fractional derivatives and may be useful for specialists in the field of hydrogeology, the oil and gas industry, and other related fields.
convergence , filtration , fractional differential equations , heterogeneous porous medium , stability , variable order of fractional derivative
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Department of Mathematics, Higher School of IT and Natural Sciences, Sarsen Amanzholov East Kazakhstan University, 148 Shakarim Ave., Ust-Kamenogorsk, 070002, Kazakhstan
Institute of Information and Computational Technologies, 28 Shevchenko Str., Almaty, 050010, Kazakhstan
Department of Mathematics
Institute of Information and Computational Technologies
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