Existence and Ulam stability of first order nonsingular impulsive and delay integrodifferential system using a concept of the delayed matrix exponential

Abstract

In this article, we discuss the existence and uniqueness of the solution along with β–Hyers–Ulam–Rassias stability of nonsingular impulsive delay integro differential system via the fixed point method. The aforementioned investigations are carried out on compact intervals and then the results are extended to unbounded intervals. We utilize Banach fixed point theorem and Gronwall’s type inequality as a main tool to ¨ achieve our desired objectives. At the end, we provide an example along with graphical representation to verify the applicability of the reported results.