Fractional Non-Markovian effect and Newton's 2nd law of motion

TL;DR

This paper investigates the dynamics of fractional Brownian motion systems, revealing non-Markovian effects due to fractional properties, yet showing that their motion still aligns with Newton's classical laws.

Contribution

It provides a detailed analysis demonstrating that fractional Brownian motion systems exhibit non-Markovian effects but follow Newtonian dynamics despite their anomalous fractional characteristics.

Findings

Non-Markovian effects are prevalent in fractional Brownian motion.

The dynamics of fBm systems are consistent with Newton's second law.

Fractional properties do not alter the fundamental Newtonian nature of the motion.

Abstract

We report in this paper a thorough study on the the dynamical mechanics of the fractional Brownian motion systems. Where several non-trivial properties are revealed such as the abundant non-Markovian effects resulted from the fractional characters of the system. In general, the dynamics of the fBm system is found to be of a purely Newton's type, despite of the anomalous fractional properties of the system.