New Retarded Nonlinear Integral Inequalities of the Gronwall-Bellman-Pachpatte Type and Their Applications

TL;DR

This paper introduces new retarded nonlinear integral inequalities of Gronwall-Bellman-Pachpatte type, generalizing existing results and enabling advanced analysis of integral and integro-differential equations.

Contribution

It presents novel retarded nonlinear inequalities that extend classical results, with applications demonstrating their effectiveness in analyzing complex equations.

Findings

New inequalities generalize classical results

Applications show improved analysis of integral equations

Framework aids in qualitative and quantitative investigations

Abstract

The goal of the present article is to offer a number of new retarded nonlinear inequalities of Gronwall, Bellman and Pachpatte kind for a class of integral and integro-differential equations. These inequalities generalize and provide new formulations of some well-known results in the mathematical framework of integral and differential inequalities that have been derived currently as well as in earlier times. These results can be utilized to investigate diverse aspects, both qualitative and quantitative, of a class of aforementioned equations. We propose a few applications to ensure effectiveness of these inequalities.