Difference schemes for the diffusion equation of fractional order with lumped heat capacity of the boundary conditions

In this work the difference scheme for the diffusion equation of fractional order with lumped heat capacity of the boundary conditions is presented. In an a priori estimate for solutions of the difference problem in the uniform metric, which implies the convergence of a solution of the problem to solving the differential problem in the uniform metric speeds $O (h^2/\tau^{\alpha-1} + \tau^{\alpha})$, $h^2 = o(\tau^{\alpha-1})$, where $\tau$, $h$ are grid steps in time and space coordinate.