This paper is concerned to establish an advanced form of the well-known Hermite-Hadamard (HH) inequality for recently-defined Generalized Conformable (GC) fractional operators. This form of the HH inequality combines various versions (new and old) of this inequality, containing operators of the types Katugampula, Hadamard, Riemann-Liouville, conformable and Riemann, into a single form. Moreover, a novel identity containing the new GC fractional integral operators is proved. By using this identity, a bound for the absolute of the difference between the two rightmost terms in the newly-established Hermite-Hadamard inequality is obtained. Also, some relations of our results with the already existing results are presented. Conclusion and future works are presented in the last section.

中文翻译：

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新广义一致分数算子的Hermite-Hadamard不等式

本文关注的是为最近定义的广义适形（GC）小数运算符建立著名的Hermite-Hadamard（HH）不等式的高级形式。HH不等式的这种形式将这种不等式的各种版本（新旧）组合在一起，其中包含Katugampula，Hadamard，Riemann-Liouville，conformable和Riemann类型的运算符。此外，证明了包含新的GC分式积分算子的新身份。通过使用该标识，可以得到新建立的Hermite-Hadamard不等式中两个最右边项之间的绝对差的界。此外，还介绍了我们的结果与现有结果之间的一些关系。结论和未来的工作在最后一部分中介绍。