  The fundamental solution (Green function) for the Cauchy problem of the
space-time fractional diffusion equation is investigated with respect to its
scaling and similarity properties, starting from its Fourier-Laplace
representation. Then, by using the Mellin transform, a general representation
of the Green function in terms of Mellin-Barnes integrals in the complex plane
is derived. This allows us to obtain a suitable computational form of the Green
function in the space-time domain and to analyse its probability
interpretation.
