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New retarded nonlinear integral inequalities of Gronwall-Bellman-Pachpatte type and their applications

Kale Nagesh

Journal of Applied Analysis

2024

Vol. 30, nr 2

379--391

The goal of the present article is to offer several 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 the effectiveness of these inequalities.