  The fundamental solution of the fractional diffusion equation of distributed
order in time (usually adopted for modelling sub-diffusion processes) is
obtained based on its Mellin-Barnes integral representation. Such solution is
proved to be related via a Laplace-type integral to the Fox-Wright functions. A
series expansion is also provided in order to point out the distribution of
time-scales related to the distribution of the fractional orders. The results
of the time fractional diffusion equation of a single order are also recalled
and then re-obtained from the general theory.
