An Existence Study on the Fractional Coupled Nonlinear $q$-Difference Systems via Quantum Operators along with Ulam–Hyers and Ulam–Hyers–Rassias Stability

Abstract

In this paper, we study the existence of solutions and their uniqueness and different kinds of Ulam–Hyers stability for a new class of nonlinear Caputo quantum boundary value problems. Also, we investigate such properties for the relevant generalized coupled q -system involving fractional quantum operators. By using the Banach contraction principle and Leray-Schauder’s fixed–point theorem, we prove the existence and uniqueness of solutions for the suggested fractional quantum problems. The Ulam–Hyers stability of solutions in different forms are studied. Finally, some examples are provided for both q -problem and coupled q -system to show the validity of the main results.