  Equation for anomalous diffusion in momentum space, recently obtained in the
recent paper (S.A. Trigger, ArXiv 0907.2793 v1, [cond-matt. stat.-mech.], 16
July 2009) is solved for the stationary and non-stationary cases on basis of
the appropriate probability transition function (PTF). Consideration of
diffusion for heavy particles in a gas of the light particles can be
essentially simplified due to small ratio of the masses of the particles.
General equation for the distribution of the light particles, shifted in
velocity space, is also derived. For the case of anomalous diffusion in
momentum space the closed equation is formulated for the Fourier-component of
the momentum distribution function. The effective friction and diffusion
coefficients are found also for the shifted distribution. If the appropriate
integrals are finite the equations derived in the paper are applicable for both
cases: the PT-function with the long tails and the short range PT-functions in
momentum space. In the last case the results are equivalent to the
Fokker-Planck equation. Practically the new results of this paper are
applicable to strongly non-equilibrium physical systems.
