In this paper, we establish some new delay Gronwall–Bellman integral inequalities with power, which can be used as a convenient tool to study the qualitative properties of solutions to differential and integral equations. We also give some examples to illustrate the application of our results to obtain the estimation for the solution of the integral and differential equations.

中文翻译：

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一类新的非线性Gronwall-Bellman延迟积分不等式与幂及其应用

在本文中，我们建立了一些新的带幂延滞的Gronwall-Bellman积分不等式，可以用作研究微分方程和积分方程解的定性性质的便捷工具。我们还给出一些例子来说明我们的结果在获得积分方程和微分方程解的估计中的应用。