On the Bielecki–Ulam’s Type Stability Results of First Order Non-linear Impulsive Delay Dynamic Systems on Time Scales

Abstract

In this manuscript, we present the existence and uniqueness of solution of first order non-linear impulsive delay dynamic systems on time scales, with the help of fixed point approach. Further, we investigate the Bielecki–Ulam–Hyers stability and Bielecki–Ulam–Hyers–Rassias stability of the proposed model. We use Gronwall’s inequality on time scales, Banach contraction principle, Picard operator and Lipschitz condition as a basic tools to develop our main results. Also, two examples are provided to illustrate the obtained results.