On Some New Nonlinear Retarded Integral Inequalities with Iterated Integrals and their Applications in Integro-Differential Equations
A. Abdeldaim *
Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, Egypt.
A. A. El-Deeb
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884),Cairo, Egypt.
*Author to whom correspondence should be addressed.
Abstract
In this paper, some new generalized retarded nonlinear integral inequalities of Gronwall-Bellman type are discussed. The upper bounds estimation of the embedded unknown functions are discussed by integral and differential techniques. Our results generalize some inequalities of H. El-Owaidy et al. [1] with both retard and nonlinear integral. Some applications are also presented in order to illustrate the usefulness of some of our results.
Keywords: Retarded integral inequalities, estimation, iterated integrals, analysis technique, integrodifferential equations