Abstract The key purpose of this study is to suggest a new fractional extension of Hermite–Hadamard, Hermite–Hadamard–Fejér and Pachpatte-type inequalities for harmonically convex functions with exponential in the kernel. Taking into account the new operator, we derived some generalizations that capture novel results under investigation with the aid of the fractional operators. We presented, in general, two different techniques that can be used to solve some new generalizations of increasing functions with the assumption of convexity by employing more general fractional integral operators having exponential in the kernel have yielded intriguing results. The results achieved by the use of the suggested scheme unfold that the used computational outcomes are very accurate, flexible, effective and simple to perform to examine the future research in circuit theory and complex waveforms.

中文翻译：

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核中具有指数的分数积分算子的一些新扩展及其在物理系统中的应用

摘要 本研究的主要目的是为核中具有指数的调和凸函数提出 Hermite-Hadamard、Hermite-Hadamard-Fejér 和 Pachpatte 型不等式的新分数扩展。考虑到新算子，我们得出了一些概括，在分数算子的帮助下捕获了正在研究的新结果。总的来说，我们提出了两种不同的技术，它们可用于通过使用在核中具有指数的更一般的分数积分算子来求解具有凸性假设的递增函数的一些新泛化，并产生了有趣的结果。使用建议方案获得的结果表明，所使用的计算结果非常准确、灵活、