On existence results of coupled pantograph discrete fractional order difference equations with numerical application

Abstract

The goal of this article is to study the existence and unique solutions of coupled pantograph discrete fractional order difference equations. The Banach contraction principal method and fixed point theorems are used to prove the existence and uniqueness criterion of the suggested coupled system associated with a discrete fractional operator in the Caputo sense. In addition, stability analysis for the considered discrete pantograph fractional order coupled system is investigated by Hyers–Ulam theoretical approach. Finally, as an application, an example is presented to illustrate the obtained results.