COMPUTER SCIENCE. CALCULATION EQUIPMENT. MANAGEMENT

A priori estimate for solution of the third boundary value problem for the fractional Halliers' equation

Ph. A. Karova

Institute of Applied Mathematics and Automation – branch of the FSBSE "Federal Scientific Center "Kabardin-Balkar Scientific Center of the Russian Academy of Sciences", 360000, KBR, Nalchik, Shortanov street, 89 A

Abstract: Moisture movement in capillary porous media is described by the equation of Halliers' [1]. Boundary value problems for classical Halliers' equation are studied in paper [2]. However, in describing the properties of the moisture movement process in media with fractal structure, the models described by the fractional equations are most effective. Solution of boundary value problem for the fractional Halliers' equation in differential setting is studied. By using the method of energy inequalities for the solution of the problem we obtain a priori estimates.

Keywords: fractional derivative, a priori estimate, Halliers' equation.

UDC: 519.633

Received: 23.11.2018

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