Department of Mathematics, University of Constantine 1 Brothers Mentouri,
BP, 325, Ain El Bey Street, 25017,
Algeria.
E-mail: ammar_boudeliou@umc.edu.dz

Abstract:

In this paper, we investigate a certain class of nonlinear Gronwall-Bellman type integral inequalities with power in more general cases involving retarded term and more general nonlinearities. Our results generalize some known integral inequalities and other results obtained very recently. The inequalities given here can be used to estimate the bound on the solutions of retarded integral equation of Volterra type and integro-differential equations (IDE) with power. Two examples are given to show the validity of our established theorems.

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