Boundedness and Continuous Dependence of Solutions for Fractional Difference Equations with Nonlocal Condition

Abstract

This study investigates the properties of solutions to nonlinear nonlocal fractional difference equations. By applying the Leray-Schauder alternative in combination with Bihari’s integral inequality, we establish rigorous results con cerning boundedness and continuous dependence of solutions on initial data. The theoretical findings are further illustrated with examples, demonstrating the practical relevance and applicability of the proposed approach. These results provide a comprehensive framework for analyzing nonlinear fractional discrete systems with nonlocal conditions and offer a foundation for future research in this area.