  A method for numerical approximation of a new class of fractional parabolic
stochastic evolution equations is introduced and analysed. This class of
equations has recently been proposed as a space-time extension of the
SPDE-method in spatial statistics. A truncation of the spectral basis function
expansion is used to discretise in space, and then a quadrature is used to
approximate the temporal evolution of each basis coefficient. Strong error
bounds are proved both for the spectral and temporal approximations. The method
is tested and the results are verified by several numerical experiments.
