  We deal with the Cauchy problem for the space-time fractional diffusion-wave
equation, which is obtained from the standard diffusion equation by replacing
the second-order space derivative with a Riesz-Feller derivative of order alpha
in (0,2] and skewness theta, and the first-order time derivative with a Caputo
derivative of order beta in (0,2]. The fundamental solution is investigated
with respect to its scaling and similarity properties, starting from its
Fourier-Laplace representation. By using the Mellin transform, we provide a
general representation of the solution in terms of Mellin-Barnes integrals in
the complex plane, which allows us to extend the probability interpretation
known for the standard diffusion equation to suitable ranges of the relevant
parameters alpha and beta. We derive explicit formulae (convergent series and
asymptotic expansions), which enable us to plot the corresponding spatial
probability densities.
