Some new integral inequalities and their applications in studying the stability of nonlinear integro-differential equations with time delay

In this paper, we generalize some integral inequalities to more general situations, and the inequalities of Pachpatte type are corollaries of ourʹs. We establish bounds on the solutions, and we show the usefulness of our results in investigating the asymptotic behavior and the stability on the solutions of integral equations, differential equations and integro-differential equations with time delay.