Fokker-Planck Equation with Fractional Coordinate Derivatives

Abstract

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to fast variable is used. The main assumption is that the correlator of probability densities of particles to make a step has a power-law dependence. As a result, we obtain Fokker-Planck equation with fractional coordinate derivative of order $1<\alpha<2$.