Difference methods for solving non-local boundary value problems for fractional-order pseudo-parabolic equations with the Bessel operator

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.