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We consider difference schemes for the time-fractional diffusion equationwith variable coefficients and nonlocal boundary conditions containing realparameters $\alpha$, $\beta$ and $\gamma$. By the method of energyinequalities, for the solution of the difference problem, we obtain a prioriestimates, which imply the stability and convergence of these differenceschemes. The obtained results are supported by the numerical calculationscarried out for some test problems.

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