In this paper, by using the theory of local fractional calculus and some techniques of real analysis, the structural characteristics of Hilbert-type local fractional integral inequalities with abstract homogeneous kernel are studied. At the same time, the necessary and sufficient conditions for these inequalities to take the best constant factor are discussed. As an application, some best constant factor inequalities with specific kernels are obtained.

中文翻译：

---

具有抽象齐次核的Hilbert型局部分数积分不等式的结构特征及其应用

本文利用局部分数阶微积分的理论和一些实分析技术，研究了具有抽象齐次核的Hilbert型局部分数阶积分不等式的结构特征。同时讨论了这些不等式取最佳常数因子的充要条件。作为一个应用，获得了一些具有特定核的最佳常数因子不等式。