Fractional Particle with Fractional First Derivatives

TL;DR

This paper introduces a novel fractional particle model with fractional first derivatives, extending classical mechanics, deriving equations of motion, analyzing symmetries, and solving key examples analytically.

Contribution

It presents the first classical fractional particle model incorporating fractional first derivatives, expanding the theoretical framework of fractional mechanics.

Findings

Derived equations of motion for the fractional particle model

Analyzed symmetries within the fractional framework

Provided analytical solutions for free and forced fractional particles

Abstract

In this paper, we introduce a new classical fractional particle model incorporating fractional first derivatives. This model represents a natural extension of the standard classical particle with kinetic energy being quadratic in fractional first derivatives and fractional linear momenta, similarly to classical mechanics. We derive the corresponding equations of motion and explore the symmetries of the model. Also, we present the formulation in terms of fractional potentials. Two important examples are analytically solved: the free particle and the particle subjected to generalized forces characterized by fractional first derivatives.