Abstract
Since the need to investigate many aspects of q-dierence equations cannot be ruled out, this article aims to explore response of the mechanism modelled by linear and nonlinear q-difference equations. Therefore, analysis of an important bundle of nonlinear q-difference equations, in particular the q-Bernoulli difference equation, has been developed. In this context, capturing the behaviour of the q-Bernoulli difference equation as well as linear q-difference equations are considered to be a significant contribution here. Illustrative examples related to the difference equations are also presented.
Highlights
Discretization of differential equations is an essential and necessary step in capturing the discrete behavior of the processes governed by the corresponding equations
One can consider an effective q-discretization based on geometric progression rather than conventional discretization regarding arithmetic progression. This approach gives rise to q-difference equations in which differential equations are encountered as q → 1. q-Difference equations are important models for representing a large number of physical events encountered in various fields of science [1–8]
Since some natural processes are represented by linear or mostly nonlinear q-difference equations, a broad range of attention has been paid on the discovery of the behavior of the corresponding processes
Summary
Discretization of differential equations is an essential and necessary step in capturing the discrete behavior of the processes governed by the corresponding equations. One can consider an effective q-discretization based on geometric progression rather than conventional discretization regarding arithmetic progression. This approach gives rise to q-difference equations in which differential equations are encountered as q → 1. There are important studies in the literature [20–26] on linear and nonlinear q-difference equations, the need to investigate many aspects of these topics cannot be ignored. Albeit small, an important bundle of nonlinear q-difference equations, in particular q-Bernoulli difference equation, will form the main backbone of this study. The q-Bernoulli difference equation, as well as linear q-difference equations, has been considered in order to make a significant contribution here
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