This article is aimed at studying novel generalizations of Hermite-Mercer-type inequalities within the Riemann-Liouville -fractional integral operators by employing -convex functions. Two new auxiliary results are derived to govern the novel fractional variants of Hadamard-Mercer-type inequalities for differentiable mapping whose derivatives in the absolute values are convex. Moreover, the results also indicate new lemmas for , , and and new bounds for the Hadamard-Mercer-type inequalities via the well-known Hölder’s inequality. As an application viewpoint, certain estimates in respect of special functions and special means of real numbers are also illustrated to demonstrate the applicability and effectiveness of the suggested scheme.

中文翻译：

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- Hermite-Mercer 型不等式的分数变体通过 -Convexity with Applications

本文旨在研究黎曼-刘维内厄米-默瑟型不等式的新颖一般化-通过使用分数次积分算-凸函数。导出了两个新的辅助结果，用于控制绝对值中的导数是凸的可微映射的 Hadamard-Mercer 型不等式的新分数变体。此外，研究结果还表明新的引理，，和 以及通过著名的 Hölder 不等式得到的 Hadamard-Mercer 型不等式的新边界。作为应用的观点，还说明了对特殊函数和实数特殊手段的某些估计，以证明所建议方案的适用性和有效性。