A difference method of solving the Steklov nonlocal boundary value   problem of the second kind for the time-fractional diffusion equation
  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. 
A. A. Alikhanov
math.NA