Finite-Time Stability of Solutions for Nonlinear $q$-Fractional Difference Coupled Delay Systems

Abstract

In this paper, we investigate and prove a new discrete q -fractional version of the coupled Gronwall inequality. By applying this result, the finite-time stability criteria of solutions for a class of nonlinear q -fractional difference coupled delay systems are obtained. As an application, an example is provided to demonstrate the effectiveness of our result.

Existence Results and Finite-Time Stability of a Fractional (p,q)-Integro-Difference System

“…(p, q)-difference calculus, also known as quantum calculus, is a well-established field that has demonstrated a wide range of applications in quantum mechanics, particle physics, hypergeometric series, and complex analysis. In the past few years, several studies have focused on examining the fractional problems involving q-difference or (p, q)-difference (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and the references therein) and we suggest that readers seeking a general overview of fractional q-calculus refer to [18,19].…”