The goal of this paper is to derive some new variants of Simpson’s inequality using the class of -polynomial convex functions of higher order. To obtain the main results of the paper, we first derive a new generalized fractional integral identity utilizing the concepts of Katugampola fractional integrals. This new fractional integral identity will serve as an auxiliary result in the development of the main results of this paper.

中文翻译：

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利用Katugampola分数阶积分通过高阶多项式凸函数的辛普森不等式的界

本文的目的是使用-高阶多项式-凸函数来推导Simpson不等式的一些新变体。为了获得本文的主要结果，我们首先利用Katugampola分数积分的概念来推导新的广义分数积分恒等式。这个新的分数积分恒等式将作为本文主要结果发展的辅助结果。