Dual Conformable Derivative: Definition, Simple Properties and Perspectives for Applications

TL;DR

This paper introduces the dual conformable derivative, explores its properties, and discusses potential applications in generalized statistical mechanics and position-dependent models.

Contribution

It defines the dual conformable derivative, analyzes its properties, and highlights its relevance for applications in physics and complex systems.

Findings

The dual conformable derivative's basic properties are established.

The q-exponential is identified as its eigenfunction.

Potential applications in position-dependent models are discussed.

Abstract

In this communication, one shows that there exists in the literature a certain form of deformed derivative that can here be identified as the dual of conformable derivative. The deformed subtraction is used here, together with the duality concept, as the basic definitions and starting points in order to obtain the connected dual operators. The q-exponential, in the context of generalized statistical mechanics, is the eigenfunction of this dual conformable derivative. The basic properties of the dual deformed-derivatives and also some perspective of applications and simple models are presented. The importance of this deformed derivative for position-dependent models is highlighted. An outlook of potential applications and developments is presented.