Controllability and Hyers–Ulam stability results of implicit coupled fractional Q-difference system of order α ∈ (1,2)

This paper deals with the controllability and Hyers–Ulam(HU) stability results of an implicit coupled fractional q-difference system with order α∈(1,2). By employing tools from fixed point theory, nonlinear functional analysis and the theory of q-calculus, we establish sufficient conditions for the existence and uniqueness of solutions, as well as controllability and stability criteria for the considered system. In particular, the Banach fixed point theorem is used to derive controllability results, while the Schauder fixed point theorem is applied to study the existence of at least one solution and HU stability. In the end, some illustrative examples are presented to demonstrate the applicability of the obtained theoretical results.