A Nonlinear Weakly Singular Retarded Henry-Gronwall Type Integral Inequality and Its Application

Nonlinear Retarded Integral Inequalities of Gronwall–bellman Type and Applications

The aim of this paper is to establish some new nonlinear retarded integral inequalities of Gronwall-Bellman type. More accurately we extend certain results which have been proved in El-Owaidy et. al, [12] and Abdeldaim and Yakout [2] to some nonlinear retarded integral inequalities. We also give some applications to estimate the solutions of some nonlinear retarded differential equations to ill...

Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method

‎In this paper‎, ‎a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{beta}(t-s)^{-alpha}G(y(s))$ based on the Tau method‎. ‎In this method‎, ‎a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution‎. ‎Error analysis of this method is also ...

On a weakly singular integral equation and its application

A direct function theoretic method is applied to solve a weakly singular integral equation whose kernel involves logarithmic singularity. This method avoids the occurrence of strong singularity. The solution of this integral equation is then applied to re-investigate the well known problem of water wave scattering by a partially immersed vertical barrier. c © 2008 Published by Elsevier Ltd

Generalized Retarded Integral Inequalities of Gronwall Type and Applications

The integral inequalities occupy privileged position in the theory of differential and integral equations. In the recent years nonlinear integral inequalities have received considerable attention because of their important applications to a variety of problems in diverse fields of nonlinear differential and integral equations. In 1919, Gronwall [4] introduced the famous Gronwall inequality in t...

An Impulsive Nonlinear Singular Version of the Gronwall-bihari Inequality