Fractional Systems and Fractional Bogoliubov Hierarchy Equations

TL;DR

This paper develops a fractional calculus framework for classical mechanics, introducing fractional phase space, Hamilton equations, and hierarchy equations, to explore systems with fractional dynamics and their statistical properties.

Contribution

It introduces fractional generalizations of phase space, Hamilton equations, and Bogoliubov hierarchy equations, extending classical mechanics into fractional calculus domain.

Findings

Derived fractional Bogoliubov hierarchy equations from fractional Liouville equation.

Proposed fractional analogs of the Vlasov equation and Debye radius.

Defined fractional reduced distribution functions.

Abstract

We consider the fractional generalizations of the phase volume, volume element and Poisson brackets. These generalizations lead us to the fractional analog of the phase space. We consider systems on this fractional phase space and fractional analogs of the Hamilton equations. The fractional generalization of the average value is suggested. The fractional analogs of the Bogoliubov hierarchy equations are derived from the fractional Liouville equation. We define the fractional reduced distribution functions. The fractional analog of the Vlasov equation and the Debye radius are considered.