  In this paper we present in one-dimensional space a numerical solution of a
partial differential equation of fractional order. This equation describes a
process of anomalous diffusion. The process arises from the interactions within
the complex and non-homogeneous background. We presented a numerical method
which bases on the finite differences method. We considered pure initial and
boundary-initial value problems for the equation with the Riesz-Feller
fractional derivative. In the final part of this paper sample results of
simulation were shown.
