An asymptotic preserving scheme for Lévy-Fokker-Planck equation with fractional diffusion limit

An asymptotic-preserving scheme for linear kinetic equation with fractional diffusion limit

A structure preserving scheme for the Kolmogorov-Fokker-Planck equation

Article history: Received 11 March 2016 Received in revised form 4 November 2016 Accepted 5 November 2016 Available online 21 November 2016

Fokker–Planck equation with fractional coordinate derivatives

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,...

Fractional Fokker-Planck equation for fractal media.

We consider the fractional generalizations of equation that defines the medium mass. We prove that the fractional integrals can be used to describe the media with noninteger mass dimensions. Using fractional integrals, we derive the fractional generalization of the Chapman-Kolmogorov equation (Smolukhovski equation). In this paper fractional Fokker-Planck equation for fractal media is derived f...

Fokker Planck Equation for Fractional Systems

The normalization condition, average values, and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A fractional (power) system is described by the fractional powers of coordinates and momenta. These systems can be considered as non-Hamiltonian systems in the usu...