On $n$-Nonlinear Caputo Fractional $q$-Differential Systems

Abstract

This paper discusses the significance of quantum calculus in some
mathematical fields. It specifically investigates solutions' existence,
uniqueness, and stability for a system of $n$-nonlinear fractional $q$%
-differential equations with initial conditions involving Caputo fractional $%
q$-derivatives. The paper utilizes Schauder's and Banach's fixed-point
theorems and Ulam-Hyers' stability criteria to explore the analytical
dynamics inherent in these solutions. Additionally, it provides two
illustrative examples to demonstrate the practical applicability of the
obtained results.