Fractional kinetic hierarchies and intermittency

TL;DR

This paper develops a framework for fractional kinetic dynamics in particle systems using convolutional derivatives, exploring intermittency phenomena through Vlasov-type hierarchies and subordination principles.

Contribution

It introduces a novel approach to fractional statistical dynamics in continuum particle systems via convolutional derivatives and Vlasov hierarchies, highlighting conditions for intermittency.

Findings

Conditions for intermittency in fractional kinetic dynamics identified

Constructed kinetic fractional dynamics using subordination principle

Linked fractional dynamics to solutions of Vlasov-type hierarchies

Abstract

We consider general convolutional derivatives and related fractional statistical dynamics of continuous interacting particle systems. We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum in terms of solutions to Vlasov-type hierarchies. Conditions for the intermittency property of fractional kinetic dynamics are obtained.