Transport Equations from Liouville Equations for Fractional Systems
arXiv:cond-mat/0604058 · doi:10.1142/S0217979206033267
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.
arXiv comment11 pages, LaTeX
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- Continuous Limit of Discrete Systems with Long-Range Interaction
- Anisotropic Fractal Media by Vector Calculus in Non-Integer Dimensional Space
- Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches
- Map of Discrete System into Continuous
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- Psi-Series Solution of Fractional Ginzburg-Landau Equation
- Fractional Liouville Equation on Lattice Phase-Space
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