By using Yang’s local fractional calculus theory, the method of weight function, and real-analysis techniques in the fractal set, a general Hilbert-type local fractional integral inequality with the kernel of a hyperbolic cosecant function is established. The necessary and sufficient condition for the constant factor of the general Hilbert-type local fractional integral inequality to be the best possible is discovered. Furthermore, two equivalent inequalities with the best constant factors were obtained.

中文翻译：

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以双曲余割函数为核的希尔伯特型局部分数阶积分不等式

利用杨氏局部分数阶微积分理论、权函数法和分形集实数分析技术，建立了以双曲余割函数为核的一般希尔伯特型局部分数积分不等式。发现了一般Hilbert型局部分数积分不等式的常数因子最优的充要条件。此外，还得到了两个具有最佳常数因子的等价不等式。