The main goal of this paper is to set up some new estimates of a specific class of dynamic integral inequalities (DII) which are partially linear on a time scale $\mathbb{T}$ with two independent variables. These, from the one hand, sum up and, on the other hand, offer a helpful method for both the qualitative and quantitative study of dynamic equations on time scales. Some applications are taken into consideration to show the validity of the fundamental results.

中文翻译：

---

基于二维时标理论的动力积分不等式的推导

本文的主要目标是建立特定类别的动态积分不等式（DII）的一些新估计，它们在带有两个自变量的时间标度$ \ mathbb {T} $上是部分线性的。一方面，这些总结起来，另一方面，为时标上的动态方程的定性和定量研究提供了一种有用的方法。考虑了一些应用以显示基本结果的有效性。