Generalizations of Gronwall-Bihari Inequalities on Time Scales

TL;DR

This paper extends Gronwall-Bihari inequalities to dynamic equations on arbitrary time scales, providing new tools for analyzing nonlinear dynamic systems with applications demonstrated.

Contribution

It introduces generalized nonlinear integral inequalities on time scales, broadening the scope of existing inequalities and their applicability to various dynamic equations.

Findings

Extended inequalities to new classes of time scales

Provided examples illustrating applicability

Applied results to analyze nonlinear dynamic equations

Abstract

We establish some nonlinear integral inequalities for functions defined on a time scale. The results extend some previous Gronwall and Bihari type inequalities on time scales. Some examples of time scales for which our results can be applied are provided. An application to the qualitative analysis of a nonlinear dynamic equation is discussed.