Fokker-Planck Equation for Fractional Systems

Details Fokker-Planck Equation for Fractional Systems Fokker-Planck Equation for Fractional Systems

2007-10-10

arxiv.org/abs/0710.2053v1

International Journal of Modern Physics B 21 (2007) 955-967

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1142/S0217979207036771

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.

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