  This paper deals with numerical solutions to a partial differential equation
of fractional order. Generally this type of equation describes a transition
from anomalous diffusion to transport processes. From a phenomenological point
of view, the equation includes at least two fractional derivatives: spatial and
temporal. In this paper we proposed a new numerical scheme for the spatial
derivative, the so called Riesz-Feller operator. Moreover, using the finite
difference method, we show how to employ this scheme in the numerical solution
of fractional partial differential equations. In other words, we considered an
initial-boundary value problem in one dimensional space. In the final part of
this paper some numerical results and plots of simulations are shown as
examples.
