On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation

Abdeldaim, A.; El-Deeb, A.A.

doi:10.1016/j.joems.2014.12.001

On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation

Document Type : Original Article

Authors

A. Abdeldaim ¹^{, 2}
A.A. El-Deeb ³

¹ Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, Egypt

² Department of Mathematics, Faculty of Science and Humanities, Shaqra University, Dawadmi, Saudi Arabia

³ Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt

10.1016/j.joems.2014.12.001

Abstract

In this paper, we investigate some new nonlinear retarded integral inequalities of Gronwall–Bellman–Pachpatte type. These inequalities generalize some former famous inequalities and
can be used as handy tools to study the qualitative as well as the quantitative properties of solutions
of some nonlinear retarded differential and integral equations. An application is also presented to
illustrate the usefulness of some of our results in estimation of solution of certain retarded nonlinear
differential equations with the initial conditions.

Keywords