Liouville and Bogoliubov Equations with Fractional Derivatives

Understand

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.