  We present a treatment of non-Markovian character of memory by incorporating
different forms of Mittag-Leffler (ML) function, which generally arises in the
solution of fractional master equation, as different memory functions in the
Generalized Kolmogorov-Feller Equation (GKFE). The cross-over from the short
time (stretched exponential) to long time (inverse power law) approximations of
the ML function incorporated in the GKFE is proven. We have found that the GKFE
solutions are the same for negative exponential and for upto frst order
expansion of stretched exponential function for very small $\tau \rightarrow
0$. A generalized integro-differential equation form of the GKFE along with an
asymptotic case is provided.
