An existence study on the fractional coupled nonlinear \(q\)-difference systems via quantum operators along with Ulam-Hyers and Ulam-Hyers-Rassias stability (Q2086484)

Summary: 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.