The effect of deformation of special relativity by conformable derivative

TL;DR

This paper explores how special relativity is deformed using conformable derivatives, deriving velocity laws and verifying the invariance of physical laws in this new framework, with potential applications in nonlinear media.

Contribution

It formulates a deformation of special relativity using conformable derivatives and demonstrates the invariance of physical laws within this new formalism.

Findings

Derived velocity addition laws in the conformable derivative framework

Verified invariance of wave, Schrödinger, and Klein-Gordon equations

Potential applicability in nonlinear or dispersive media

Abstract

In the article, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory were re-stated. And, the addition of velocity laws were derived and used to verify the constancy of the speed of light. The invariance principle of the laws of physics is demonstrated for some typical illustrative examples, namely, the conformable wave equation, the conformable Schrodinger equation, and the conformable Gordon-Klein equation. The current formalism may be applicable when using special relativity in a nonlinear or dispersive medium.