A generalized Fokker–Planck equation for anomalous diffusion in velocity space

A more general quasi-Fokker–Planck equation is derived to describe particle kinetics in situations when the usual Fokker–Planck equation is not applicable. 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. The only assumption is smallness of the typical velocity of the particles, undergoing diffusion. The developed approach is another tool to study anomalous diffusion, avoiding conventional in such problems fractional differentiation. In this Letter anomalous diffusion in velocity space is considered for hard-sphere, Coulomb and dusty plasma collision models.

► We expand the Master equation into a series.
► We derive a generalized equation for description of anomalous diffusion.
► We consider special cases of anomalous diffusion for hard-sphere interactions, Coulomb systems and dusty plasmas.