  A generalized Fokker-Planck equation is derived to describe particle kinetics
in specific situations when the probability transition function (PTF) has a
long tail in momentum space. The equation is valid for an arbitrary value of
the transferred in a collision act momentum and for the arbitrary mass ratio of
the interacting particles. On the basis of the generalized Fokker-Planck
equation anomalous diffusion in velocity space is considered for hard sphere
model of particle interactions, Coulomb collisions and interactions typical for
dusty plasmas. The example of dusty plasma interaction is peculiar in way that
it leads to a new term in the obtained Fokker-Planck-iike equation due to the
dependence of the differential cross-section on the relative velocity. The
theory is also applied to diffusion of heavy particles in the ambience of light
particles with a prescribed power-type velocity distribution function. In
general, the theory is applicable to consideration of anomalous diffusion in
velocity space if the typical velocity of one sort of particles undergoing
diffusion is small compared to the typical velocity of the background
particles.
