ON CONTROLLABILITY, STABILITY AND SOLVABILITY OF HILFER FRACTIONAL <i>q</i>-DYNAMICAL DELAY EQUATIONS ON TIME SCALES

This article investigates a class of Hilfer-type fractional <i>q</i>-difference equations with time delay on time scales. Using Krasnoselskii's fixed point theorem and Banach contraction mapping principle, we obtain the existence and uniqueness of solutions for this equation. Meanwhile, we discuss the Hyers-Ulam stability of the solution for the equation by constructing a suitable perturbed equation, and obtain sufficient conditions of the controllability for the equation through the utilization of a non-zero bounded linear operator and a function that characterizes the control action. A numerical example is presented to validate the main results.