  We consider difference schemes for the time-fractional diffusion equation
with variable coefficients and nonlocal boundary conditions containing real
parameters $\alpha$, $\beta$ and $\gamma$. By the method of energy
inequalities, for the solution of the difference problem, we obtain a priori
estimates, which imply the stability and convergence of these difference
schemes. The obtained results are supported by the numerical calculations
carried out for some test problems.

Numerical Analysis