Existence, uniqueness and stability of solution to mixed integral dynamic systems with instantaneous and noninstantaneous impulses on time scales

Abstract

In this paper, we study the existence and uniqueness of solution and stability results of mixed integral dynamic system with instantaneous and noninstantaneous impulses on time scales, by using the fixed point method. The main tools to establish our results are the Grönwall’s inequality on time scales, Picard operator and abstract Grönwall lemma. Some assumptions are made to overcome the hurdles in achieving our results. At the end, an example is given that shows the validity of our main results.