Note on Some Nonlinear Integral Inequalities and Applications to Differential Equations
نویسنده
چکیده
Khaled Boukerrioua Department of Mathematics, University of 08 mai 1945, BP. 401, Guelma 24000, Algeria Correspondence should be addressed to Khaled Boukerrioua, [email protected] Received 29 June 2011; Accepted 12 September 2011 Academic Editor: Elena Braverman Copyright q 2011 Khaled Boukerrioua. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Using ideas from Boukerrioua and Guezane-Lakoud 2008 , some nonlinear integral inequalities are established.
منابع مشابه
Random differential inequalities and comparison principles for nonlinear hybrid random differential equations
In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities have been proved for an IVP of first order hybrid random differential equations with the linear perturbation of second type. A comparison theorem is proved and applied to prove the uniqueness of random solution for the considered perturbed random differential eq...
متن کاملPresentation of two models for the numerical analysis of fractional integro-differential equations and their comparison
In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...
متن کاملSome extensions of Darbo's theorem and solutions of integral equations of Hammerstein type
In this brief note, using the technique of measures of noncompactness, we give some extensions of Darbo fixed point theorem. Also we prove an existence result for a quadratic integral equation of Hammerstein type on an unbounded interval in two variables which includes several classes of nonlinear integral equations of Hammerstein type. Furthermore, an example is presented to show the effic...
متن کاملSome new results using Hadamard fractional integral
Fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order. The purpose of this work is to use Hadamard fractional integral to establish some new integral inequalities of Gruss type by using one or two parameters which ensues four main results . Furthermore, other integral inequalities of reverse ...
متن کاملSome Nonlinear Weakly Singular Integral Inequalities with Two Variables and Applications
Various singular integral inequalities play an important role in the development of the theory of differential equations, functional differential equations, and integral equations. For example, Henry 1 proposed a linear integral inequality with singular kernel to investigate some qualitative properties for a parabolic differential equation, and Sano and Kunimatsu 2 gave a modified version of He...
متن کامل