  In this study, we analytically formulated the path integral representation of
the conditional probabilities for non-Markovian kinetic processes in terms of
the free energy of the thermodynamic system. We carry out analytically the
time-fractional kinetic equations for these processes. Thus, in a simple way,
we generalize path integral solutions of the Markovian to the non-Markovian
cases. We conclude that these pedagogical results can be applied to some
physical problems such as the deformed ion channels, internet networks and
non-equilibrium phase transition problems.
