  In the present Short Note an idea is proposed to explain the emergence and
the observation of processes in complex media that are driven by fractional
non-Markovian master equations. Particle trajectories are assumed to be solely
Markovian and described by the Continuous Time Random Walk model. But, as a
consequence of the complexity of the medium, each trajectory is supposed to
scale in time according to a particular random timescale. The link from this
framework to microscopic dynamics is discussed and the distribution of
timescales is computed. In particular, when a stationary distribution is
considered, the timescale distribution is uniquely determined as a function
related to the fundamental solution of the space-time fractional diffusion
equation. In contrast, when the non-stationary case is considered, the
timescale distribution is no longer unique. Two distributions are here
computed: one related to the M-Wright/Mainardi function, which is Green's
function of the time-fractional diffusion equation, and another related to the
Mittag-Leffler function, which is the solution of the fractional-relaxation
equation.
