  An unsteady problem is considered for a space-fractional diffusion equation
in a bounded domain. A first-order evolutionary equation containing a
fractional power of an elliptic operator of second order is studied for general
boundary conditions of Robin type. Finite element approximation in space is
employed. To construct approximation in time, regularized two-level schemes are
used. The numerical implementation is based on solving the equation with the
fractional power of the elliptic operator using an auxiliary Cauchy problem for
a pseudo-parabolic equation. The results of numerical experiments are presented
for a model two-dimensional problem.
