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

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