  Delay Gronwall inequality with a weakly singular kernel has been a subject of
interest in various mathematical studies. In this article, we will delve into
the consideration of this inequality and its application in the study
continuity of the state trajectory for a Volterra integral equation with delay.
Using delay Gronwall inequality with a singular kernel, we investigate the
behavior and properties of the state trajectory if there are delays. This
analysis aims to improve our understanding of the dynamics associated in del
Volterra integral equations with delay. In addition, we present a comprehensive
example demonstrating the practical significance of our results.
