Fokker-Planck Equation for Fractional Systems
Statistical Mechanics
2009-11-13 v1
Abstract
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 usual phase space. The generalizations of the Bogoliubov equations are derived from the Liouville equation for fractional (power) systems. Using these equations, the corresponding Fokker-Planck equation is obtained.
Keywords
Cite
@article{arxiv.0710.2053,
title = {Fokker-Planck Equation for Fractional Systems},
author = {Vasily E. Tarasov},
journal= {arXiv preprint arXiv:0710.2053},
year = {2009}
}