Controllability of Impulsive Non–Linear Delay Dynamic Systems on Time Scale

Akbar Zada,Gohar Ali,Jehad Alzabut,Luqman Alam,Wiyada Kumam,Poom Kumam

doi:10.1109/access.2020.2995328

Abstract

In this paper, we obtain the results of controllability for first order impulsive non-linear time varying delay dynamic systems and Hammerstein impulsive system on time scale, using the theory of fixed points such as Banach fixed point theorem combined with Lipchitz conditions and non linear functional analysis. We also provide examples to support our theoretical results.

Highlights

The theory of differential equations with impulses has been well utilized in mathematical modeling
Zada et al.: Controllability of Impulsive Non–Linear Delay Dynamic Systems on Time Scale stability [32]–[34], is related to the difference between the exact and approximate solutions of the considered problem, and this concept can be used in approximation theory and numerical analysis
In this paper, we established the controllability of systems (1) and (2)

Summary

Introduction

The theory of differential equations with impulses has been well utilized in mathematical modeling. For more results on the controllability of impulsive systems one can see the work of Shubov et al [15] and Park et al [16]. Many researchers discussed the existence, uniqueness, stability and controllability of abstract equations on time scale.

Results

Conclusion