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

Anomalous Kinetics in Velocity Space: equations and models