Transport Equations from Liouville Equations for Fractional Systems

Abstract

We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the fractional systems are non-Hamiltonian. Generalized transport equation is derived from Liouville and Bogoliubov equations for fractional systems. Fractional generalization of average values and reduced distribution functions are defined. Hydrodynamic equations for fractional systems are derived from the generalized transport equation.

11 pages, LaTeX

References in corpus (3)

• Fractional Hydrodynamic Equations for Fractal Media
• Possible Experimental Test of Continuous Medium Model for Fractal Media
• Stationary Solutions of Liouville Equations for Non-Hamiltonian Systems

Cited by in corpus (6)

• Anisotropic Fractal Media by Vector Calculus in Non-Integer Dimensional Space
• Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches
• Psi-Series Solution of Fractional Ginzburg-Landau Equation
• Fractional Liouville Equation on Lattice Phase-Space
• Fokker-Planck Equation for Fractional Systems
• Generalized diffusion equation with nonlocality of space-time. Memory function modelling