Some linear and nonlinear integral inequalities on time scales in two independent variables

TL;DR

This paper develops new linear and nonlinear integral inequalities on time scales with two variables, extending classical inequalities and providing applications to dynamic equations.

Contribution

It introduces generalized integral inequalities on time scales for functions of two variables, including applications to partial delta dynamic equations.

Findings

Established new integral inequalities of Gronwall-Bellman-Bihari type on time scales.

Provided examples with specific time scales to illustrate the inequalities.

Applied results to estimate solutions of partial delta dynamic equations.

Abstract

We establish some linear and nonlinear integral inequalities of Gronwall-Bellman-Bihari type for functions with two independent variables on general time scales. The results are illustrated with examples, obtained by fixing the time scales to concrete ones. An estimation result for the solution of a partial delta dynamic equation is given as an application.