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LIOUVILLE AND BOGOLIUBOV EQUATIONS WITH FRACTIONAL DERIVATIVES

VASILY E. TARASOV

Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119992, Russia

https://doi.org/10.1142/S0217984907012700Cited by:25 (Source: Crossref)

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.

Keywords:

PACS: 05.20.-y, 05.20.Dd, 45.10.Hj

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