Grid methods for solving nonlocal boundary value problems for the convection-diffusion equation of fractional order with degeneration

Author(s):  M.KH. Beshtokov, candidate of Sciences, no, Institute of Applied Mathematics and Automation KBSC RAS,, Nalchik, Russia, beshtokov-murat@yandex.ru,

V.A. Vodakhova, candidate of Sciences, no, Kabardino-Balkarian State University, Nalchik, Russia, vodahova@yandex.ru

Issue:  Volume 51, № 3

Rubric:  Mathematics

Annotation:  In this paper we study nonlocal boundary value problems for the convection-diffusion equation of fractional order with degeneration. The main result of the work is to obtain by the method of energy inequalities a priori estimates in differential and difference interpretations for solving the problems under consideration. From the obtained estimates, the uniqueness and stability of the solution with respect to the initial data and the right part, as well as the convergence of the approximate solution to the exact, solution of the differential problem under consideration, follow

Keywords:  nonlocal boundary-value problem, a priori estimate, difference scheme, the equation of convection-diffusion differential equation of fractional order, Caputo fractional derivative

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