Superstatistics for fractional systems

TL;DR

This paper introduces a fractional dynamical framework for superstatistics, deriving superstatistical distributions from fractional Fokker-Planck equations using a generalized Bayes' theorem, with specific examples provided.

Contribution

It develops a novel fractional approach to superstatistics, connecting fractional Fokker-Planck equations with superstatistical distributions.

Findings

Derived superstatistical distributions from fractional Fokker-Planck equations.

Demonstrated the approach with specific fractional system examples.

Abstract

The purpose of this paper is to develop a new fractional dynamical approach to superstatistics. Namely, we show that superstatistical distribution functions can be obtained from stationary solutions of the generalized Fokker-Planck equation for fractional systems by using the fractional generalization Bayes' theorem. We present specific examples of such distribution functions for fractional systems.