  The aim of this paper is to numerically solve a diffusion differential
problem having time derivative of fractional order. To this end we propose a
collocation-Galerkin method that uses the fractional splines as approximating
functions. The main advantage is in that the derivatives of integer and
fractional order of the fractional splines can be expressed in a closed form
that involves just the generalized finite difference operator. This allows us
to construct an accurate and efficient numerical method. Several numerical
tests showing the effectiveness of the proposed method are presented.
