  The problem of anomalous diffusion in momentum (velocity) space is considered
based on the master equation and the appropriate probability transition
function (PTF). The approach recently developed by the author for coordinate
space, is applied with necessary modifications to velocity space. A new general
equation for the time evolution of the momentum distribution function in
momentum space is derived. This allows the solution of various problems of
anomalous transport when the probability transition function (PTF) has a long
tail in momentum space. For the opposite cases of the PTF rapidly decreasing as
a function of transfer momenta (when large transfer momenta are strongly
suppressed), the developed approach allows us to consider strongly
non-equilibrium cases of the system evolution. The stationary and
non-stationary solutions are studied. As an example, the particular case of the
Boltzmann-type PT-function for collisions of heavy and light particles with the
determined (prescribed) distribution function, which can be strongly
non-equilibrium, is considered within the proposed general approach. The
appropriate diffusion and friction coefficients are found. The Einstein
relation between the friction and diffusion coefficients is shown to be
violated in these cases.
