  Difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters $\alpha$ and $\beta$ are considered. 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. 
Stability and convergence of difference schemes approximating a   two-parameter nonlocal boundary value problem for time-fractional diffusion   equation