Gronwall–Bellman-type inequalities provide a very effective way to investigate the qualitative and quantitative properties of solutions of nonlinear integral and differential equations. In recent years, local fractional calculus has attracted the attention of many researchers. In this paper, based on the basic knowledge of local fractional calculus and the method of proving inequality on the set of real numbers, some new Gronwall–Bellman inequalities are discussed and established on the fractal space. Our results are a powerful supplement to the existing literature.

中文翻译：

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分形集上一些新型的GRONWALL-BELLMAN不等式

Gronwall-Bellman 型不等式提供了一种非常有效的方法来研究非线性积分和微分方程解的定性和定量性质。近年来，局部分数阶微积分引起了许多研究者的关注。本文基于局部分数阶微积分的基本知识和实数集上不等式的证明方法，在分形空间上讨论并建立了一些新的Gronwall-Bellman不等式。我们的结果是对现有文献的有力补充。