  It is shown that due to memory effects the complex behaviour of components in
a stochastic system can be transmitted to macroscopic evolution of the system
as a whole. Within the Markov approximation widely using in ordinary
statistical mechanics, memory effects are neglected. As a result, a time-scale
separation between the macroscopic and the microscopic level of description
exists, the macroscopic differential picture is no a consequence of microscopic
non-differentiable dynamics. On the other hand, the presence of complete memory
in a system means that all its components have the same behaviour. If the
memory function has no characteristic time scales, the correct description of
the macroscopic evolution of such systems have to be in terms of the fractional
calculus.
