Liouville and Bogoliubov Equations with Fractional Derivatives

Details Liouville and Bogoliubov Equations with Fractional Derivatives Liouville and Bogoliubov Equations with Fractional Derivatives

2007-11-06

arxiv.org/abs/0711.0859v1

Modern Physics Letters B 21 (2006) 237-248

Physics

Mathematical Physics

14 pages, LaTeX

Scientific paper

10.1142/S0217984907012700

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.

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