STUDY OF THE INITIAL BOUNDARY VALUE PROBLEM FOR A TWO-DIMENSIONAL CONVECTION-DIFFUSION EQUATION WITH A FRACTIONAL TIME DERIVATIVE IN THE SENSE OF CAPUTO-FABRIZIO

Alimbekova N.B. Oskorbin N.M.
29 June 2021 al-Farabi Kazakh State National University

KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2021 #110 Issue 2 97 - 112 pp.

In this paper, we study an initial boundary value problem for a differential equation with a fractional order derivative in time in the Caputo-Fabrizio sense. This equation is of great practical importance in modeling the processes of fluid motion in porous media and anomalous dispersion. The uniqueness and continuous dependence of the solution of the problem on the input data in differential form is proved. A computationally efficient implicit difference scheme with weights is proposed. A priori estimates are obtained for the solution of the problem under the assumption that the solution exists in the class of sufficiently smooth functions. The uniqueness of the solution and the stability of the difference scheme with respect to the initial data and the right-hand side of the equation follows from the obtained estimates. The convergence of the difference problem solution to the differential problem solution with the second order in time and space variables is proved. The results of computational experiments confirming the reliability of the theoretical analysis are presented.

a priori estimate , convergence , energy inequality method , finite difference method , fractional derivative in the sense of Caputo-Fabrizio , Fractional differential equation , stability

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Abai Kazakh National Pedagogical University, Almaty, Kazakhstan
S. Amanzholov East Kazakhstan University, Ust-Kamenogorsk, Kazakhstan
Altai State University, Barnaul, Russian Federation

Abai Kazakh National Pedagogical University
S. Amanzholov East Kazakhstan University
Altai State University

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