  An unsteady problem is considered for a space-fractional equation in a
bounded domain. A first-order evolutionary equation involves a fractional power
of an elliptic operator of second order. Finite element approximation in space
is employed. To construct approximation in time, standard two-level schemes are
used. The approximate solution at a new time-level is obtained as a solution of
a discrete problem with the fractional power of the elliptic operator. A
Pade-type approximation is constructed on the basis of special quadrature
formulas for an integral representation of the fractional power elliptic
operator using explicit schemes. A similar approach is applied in the numerical
implementation of implicit schemes. The results of numerical experiments are
presented for a test two-dimensional problem.
