In this article, firstly, Hermite–Hadamard’s inequality is generalized via a fractional integral operator associated with the Caputo–Fabrizio fractional derivative. Then a new kernel is obtained and a new theorem valid for convex functions is proved for fractional order integrals. Also, some applications of our main findings are given.

中文翻译：

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Caputo-Fabrizio型分数积分的Hermite-Hadamard不等式及相关不等式

在本文中，首先，通过与Caputo-Fabrizio分数导数相关的分数积分算子来推广Hermite-Hadamard不等式。然后得到一个新的核，并证明了对于凸函数有效的新定理，适用于分数阶积分。此外，还给出了我们主要发现的一些应用。