Difference methods for solving non-local boundary value problems for fractional-order pseudo-parabolic equations with the Bessel operator
M.K. Beshtokov
Institute of Applied Mathematics and Automation, Nalchik, Russia
Keywords: нелокальные краевые задачи, априорная оценка, разностная схема, уравнение псевдопараболического типа, дифференциальное уравнение дробного порядка, дробная производная Герасимова-Капуто, Non-local boundary value problem, a priori estimate, difference scheme, equation of pseudoparabolic type, differential equation of fractional order, Gerasimov-Caputo fractional derivative
Abstract
This paper deals with the to boundary value problems for pseudoparabolic equations of fractional order with the Bessel operator with variable coefficients with non-local boundary conditions of the integral type and difference methods for their solutions. To solve the considered problems a priori estimates in differential and difference interpretations are obtained, which means the uniqueness and stability of solutions by initial data and the right-hand side, as well as the convergence of the solution of the difference problem to the solution of the corresponding differential problem.
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