Existence and uniqueness of solutions for nonlinear Caputo fractional difference equations

Abstract

We study two cases of nabla fractional Caputo difference equations. Our main tool used is a Banach fixed pointtheorem, which allows us to give some existence and uniqueness theorems of solutions for discrete fractional Caputo equations. In addition, we develop the existence results for delta fractional Caputo difference equations, which correct ones obtained in Chen and Zhou. We present two examples to illustrate our main results.