Deformed special relativity based on $\alpha$-deformed binary operations

TL;DR

This paper introduces a fractional mechanics framework based on $eta$-deformed binary operations, defining new velocity and acceleration dimensions, and explores conservation laws and Hamiltonian formalism within this novel approach.

Contribution

It presents a new fractional mechanics model with deformed velocity and acceleration, extending classical mechanics through fractional addition rules and Hamiltonian formalism.

Findings

Defined fractional velocity and acceleration with $eta$-deformed dimensions

Established conservation of fractional energy

Formulated Hamiltonian formalism for fractional mechanics

Abstract

In this paper, we define a new velocity having a dimension of $(Length)^{\alpha}/(Time)$ and a new acceleration having a dimension of $(Length)^{\alpha}/(Time)^2$, based on the fractional addition rule. We then discuss the fractional mechanics in one dimension. We show the conservation of fractional energy, and formulate the Hamiltonian formalism for the fractional mechanics. As a matter of illustration, we exhibit some examples for the fractional mechanics.