Deriving friction force using fractional calculus

TL;DR

This paper introduces a novel method to derive friction force using fractional calculus, capturing non-uniform time flow in dissipative processes without unphysical assumptions.

Contribution

It presents a new fractional calculus-based framework for modeling friction, linking fractional derivatives to inhomogeneous velocity and energy dissipation.

Findings

Correct Euler-Lagrange equations derived

Hamilton equations obtained with fractional derivatives

Fractional term vanishes during energy measurements

Abstract

The friction force is derived using fractional calculus by considering the non-uniform flow of time in dissipative processes. The approach incorporates inhomogeneous velocity without unphysical approximations, resulting in a Lagrangian where the order of fractional derivatives measures time intervals. The fractional term in the Lagrangian provides correct Euler-Lagrange, and ultimately, the Hamilton equations, and vanishes during energy change measurements, like a ghost.