Controllability and Hyers–Ulam Stability of Differential Systems with Pure Delay

Dynamic systems of linear and nonlinear differential equations with pure delay are considered in this study. As an application, the representation solutions these help their delayed Mittag–Leffler matrix functions is used to obtain controllability Hyers–Ulam stability results. By introducing a Gramian matrix, we establish some sufficient necessary conditions for systems. In addition, by applying Krasnoselskii’s fixed point theorem, Our results improve, extend, complement existing ones. Finally, two examples given illustrate main