Fractional statistical dynamics and fractional kinetics

TL;DR

This paper develops a framework for fractional statistical dynamics using the subordination principle, leading to new kinetic equations and insights into intermittency in fractional mesoscopic systems.

Contribution

It introduces a novel approach to fractional kinetic dynamics via Vlasov-type hierarchies and derives a non-linear kinetic equation for particle density evolution.

Findings

Derived a fractional kinetic equation for particle density.

Analyzed intermittency phenomena in fractional mesoscopic dynamics.

Connected subordination principle with Vlasov-type hierarchies.

Abstract

We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum in terms of solutions to Vlasov-type hierarchies. As a by-product we obtain the evolution of the density of particles in the fractional kinetics in terms of a non-linear Vlasov-type kinetic equation. As an application we study the intermittency of the fractional mesoscopic dynamics.