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MATH MODELING. PHYSICS

A priori estimates for solutions of boundary value problems for convection-diffusion fractional-order equation

E. M. Shogenova

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: In this paper by the method of energy inequalities a priori estimates for the solution of the Dirichlet and Robin boundary value problems for the convection-diffusion equation of fractional order are obtained. From this follows the uniqueness and continuous dependence of the solution of the problems posed on the initial data.

Keywords: Caputo fractional derivative, Riemann-Liouville fractional integral, fractional convection-diffusion equation, boundary value problems, a priori estimate.

UDC: 519.633

Received: 12.10.2017