The theory of convex functions plays an important role in engineering and applied mathematics. The Caputo–Fabrizio fractional derivatives are one of the important notions of fractional calculus. The aim of this paper is to present some properties of Caputo–Fabrizio fractional integral operator in the setting of -convex function. We present some new Caputo–Fabrizio fractional estimates from Hermite–Hadamard-type inequalities. The results of this paper can be considered as the generalization and extension of many existing results of inequalities and convex functions. Moreover, we also present some application of our results to special means of real numbers.

中文翻译：

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修正凸函数的Hermite-Hadamard型的Caputo-Fabrizio分数阶积分不等式

凸函数理论在工程和应用数学中起着重要作用。Caputo–Fabrizio分数导数是分数演算的重要概念之一。本文的目的是介绍Caputo–Fabrizio分数阶积分算子在-凸函数设置中的一些性质。我们根据Hermite-Hadamard型不等式提出了一些新的Caputo-Fabrizio分数估计。本文的结果可以看作是对不等式和凸函数的许多现有结果的推广和扩展。此外，我们还介绍了我们的结果在实数的特殊方法中的一些应用。