On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation
Abdeldaim, A., El-Deeb, A. (2015). On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation. EKB Journal Management System, 23(3), 470-475. doi: 10.1016/j.joems.2014.12.001
A. Abdeldaim; A.A. El-Deeb. "On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation". EKB Journal Management System, 23, 3, 2015, 470-475. doi: 10.1016/j.joems.2014.12.001
Abdeldaim, A., El-Deeb, A. (2015). 'On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation', EKB Journal Management System, 23(3), pp. 470-475. doi: 10.1016/j.joems.2014.12.001
Abdeldaim, A., El-Deeb, A. On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation. EKB Journal Management System, 2015; 23(3): 470-475. 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

Journal of the Egyptian Mathematical Society
Volume 23, Issue 3, 2015, Page 470-475  XML PDF (450.71 K)
Document Type: Original Article
DOI: 10.1016/j.joems.2014.12.001
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Authors
A. Abdeldaim1, 2; A.A. El-Deeb* 3
1Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, Egypt
2Department of Mathematics, Faculty of Science and Humanities, Shaqra University, Dawadmi, Saudi Arabia
3Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt
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
KEYWORDS Integral inequality; Analysis technique; Estimation; Retarded integral and differential equation
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