The deformed exponential functions of two variables

TL;DR

This paper introduces two-variable deformed exponential functions, exploring their mathematical properties and potential applications in modeling continuous and discrete phenomena across physics.

Contribution

It presents new two-variable deformed exponential functions with unique differential and difference properties, advancing their mathematical understanding and applicability.

Findings

Derived differential properties of the deformed functions

Analyzed difference properties relevant to discrete models

Highlighted potential applications in physical phenomena modeling

Abstract

In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like special cases, and, even more, to acquit their inauguration from mathematical point of view. Really, we will show interesting differential and difference properties of our deformations which are important in forming and explanation of continuous and discrete models of numerous phenomena.