Fractional Generalization of Liouville Equations

Abstract

In this paper fractional generalization of Liouville equation is considered. We derive fractional analog of normalization condition for distribution function. Fractional generalization of the Liouvile equation for dissipative and Hamiltonian systems was derived from the fractional normalization condition. This condition is considered considered as a normalization condition for systems in fractional phase space. The interpretation of the fractional space is discussed.

9 pages, LaTeX

References in corpus (5)

• Quantization of non-Hamiltonian and Dissipative Systems
• Quantum Computer with Mixed States and Four-Valued Logic
• Pure Stationary States of Open Quantum Systems
• Stationary States of Dissipative Quantum Systems
• Bosonic String in Affine-Metric Curved Space

Cited by in corpus (51)

• Fractal universe and quantum gravity
• Continuous Medium Model for Fractal Media
• Fractional Ginzburg-Landau equation for fractal media
• Fractional Hydrodynamic Equations for Fractal Media
• Quantum field theory, gravity and cosmology in a fractal universe
• Continuous Limit of Discrete Systems with Long-Range Interaction
• Geometry and field theory in multi-fractional spacetime
• Fractional Generalization of Gradient and Hamiltonian Systems
• Detailed balance in Horava-Lifshitz gravity
• Anisotropic Fractal Media by Vector Calculus in Non-Integer Dimensional Space
• Fractional oscillator
• Fractional Systems and Fractional Bogoliubov Hierarchy Equations
• Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches
• Fractional Liouville and BBGKI Equations
• Gravity on a multifractal
• Fractional Fokker-Planck Equation for Fractal Media
• Wave Equation for Fractal Solid String
• Electromagnetic field of fractal distribution of charged particles
• Map of Discrete System into Continuous
• Possible Experimental Test of Continuous Medium Model for Fractal Media
• Adaptive molecular resolution via a continuous change of the phase space dimensionality
• Fractional Derivative as Fractional Power of Derivative
• Fractional Statistical Mechanics
• Phase-Space Metric for Non-Hamiltonian Systems
• Magnetohydrodynamics of Fractal Media
• Gravitational Field of Fractal Distribution of Particles
• Nonholonomic Constraints with Fractional Derivatives
• Psi-Series Solution of Fractional Ginzburg-Landau Equation
• Heterogeneous diffusion in comb and fractal grid structures
• Hamiltonian formalism of fractional systems
• Fractional diffusion on a fractal grid comb
• Transport Equations from Liouville Equations for Fractional Systems
• Multipole Moments of Fractal Distribution of Charges
• Fractional Generalization of Gradient Systems
• Dynamics of Fractal Solids
• Anomalous diffusion on a fractal mesh
• Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part two: Solar Flares dynamics
• Fractional Liouville Equation on Lattice Phase-Space
• Quenched and Annealed Disorder Mechanisms in Comb-Models with Fractional Operators
• Fokker-Planck Equation for Fractional Systems
• Stationary Solutions of Liouville Equations for Non-Hamiltonian Systems
• Generalized diffusion equation with fractional derivatives within Renyi statistics
• Fractal features in accretion discs
• Critical properties of spherically symmetric accretion in a fractal medium
• On spherically symmetrical accretion in fractal media
• Axially Symmetric Accretion of Fractal Medium onto Rotating Black Holes and the emergence of the Acoustic Manifold
• Thermodynamics of Few-Particle Systems
• Generalized diffusion equation with nonlocality of space-time. Memory function modelling
• The variant of post-Newtonian mechanics with generalized fractional derivatives
• Generalized diffusion equation with nonlocality of space-time: analytical and numerical analysis
• A consistent description of the kinetic processes of electrolyte ion transport in a dynamic porous medium