  We discuss a dynamic procedure that makes the fractional derivatives emerge
in the time asymptotic limit of non-Poisson processes. We find that two-state
fluctuations, with an inverse power-law distribution of waiting times, finite
first moment and divergent second moment, namely with the power index mu in the
interval 2<mu <3, yields a generalized master equation equivalent to the sum of
an ordinary Markov contribution and of a fractional derivative term. We show
that the order of the fractional derivative depends on the age of the process
under study. If the system is infinitely old, the order of the fractional
derivative, ord, is given by ord=3-mu . A brand new system is characterized by
the degree ord=mu -2. If the system is prepared at time -ta<0$ and the
observation begins at time t=0, we derive the following scenario. For times
0<t<<ta the system is satisfactorily described by the fractional derivative
with ord=3-mu . Upon time increase the system undergoes a rejuvenation process
that in the time limit t>>ta yields ord=mu -2. The intermediate time regime is
probably incompatible with a picture based on fractional derivatives, or, at
least, with a mono-order fractional derivative.
