On boundary value problems for fractional-order differential equations

Abstract

The article is devoted to the study of boundary value problems for a fractional-orderconvection-diffusion equation with memory effect. We construct two-layer monotone schemes withweights of the second order accuracy with respect to the time and space variables. We provethe uniqueness and stability for the solution with respect to the initial data and right-hand sideand also the convergence of the solution of the difference scheme to the solutionof the corresponding differential problem.