Fokker-Planck Equation for Fractional Systems

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.

References in corpus (7)

• Fractional Generalization of Liouville Equations
• Fractional Systems and Fractional Bogoliubov Hierarchy Equations
• Fractional Liouville and BBGKI Equations
• Fractional Fokker-Planck Equation for Fractal Media
• Transport Equations from Liouville Equations for Fractional Systems
• Classical Canonical Distribution for Dissipative Systems
• Stationary Solutions of Liouville Equations for Non-Hamiltonian Systems

Cited by in corpus (3)

• Anisotropic Fractal Media by Vector Calculus in Non-Integer Dimensional Space
• Fokker-Planck Equation with Fractional Coordinate Derivatives
• Superstatistics for fractional systems