Liouville and Bogoliubov Equations with Fractional Derivatives

Abstract

The Liouville equation, first Bogoliubov hierarchy and Vlasov equations with derivatives of non-integer order are derived. Liouville equation with fractional derivatives is obtained from the conservation of probability in a fractional volume element. This equation is used to obtain Bogoliubov hierarchy and fractional kinetic equations with fractional derivatives. Statistical mechanics of fractional generalization of the Hamiltonian systems is discussed. Fractional kinetic equation for the system of charged particles are considered.

arXiv comment14 pages, LaTeX

References in corpus (7)

• Continuous Medium Model for Fractal Media
• Nonlinear Fractional Dynamics on a Lattice with Long Range Interactions
• Fractional Generalization of Gradient and Hamiltonian Systems
• Fractional Differential Forms
• Dynamics with Low-Level Fractionality
• Coupled oscillators with power-law interaction and their fractional dynamics analogues
• Gravitational Field of Fractal Distribution of Particles

Cited by in corpus (7)

• Fractional Vector Calculus and Fractional Maxwell's Equations
• Geometry and field theory in multi-fractional spacetime
• Fractional Liouville Equation on Lattice Phase-Space
• Power-law Spatial Dispersion from Fractional Liouville Equation
• Generalized diffusion equation with fractional derivatives within Renyi statistics
• Theory on linear L-fractional differential equations and a new Mittag-Leffler-type function
• Geometry of fractional spaces