This paper aims to investigate the several generalizations by newly proposed generalized $ \mathcal{K} $-fractional conformable integral operator. Based on these novel ideas, we derived a novel framework to study for $ \breve{C} $eby$ \breve{s} $ev and P$ \acute{o} $lya-Szeg$ \ddot{o} $ type inequalities by generalized $ \mathcal{K} $-fractional conformable integral operator. Several special cases are apprehended in the light of generalized fractional conformable integral. This novel strategy captures several existing results in the relative literature. We also aim at showing important connections of the results here with those including Riemann-Liouville fractional integral operator.

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更多关于广义积分不等式的新结果 \begin{document}$ \mathcal{K} $\end{document}-分数一致积分运算符

本文旨在研究新提出的广义$ \mathcal{K} $-分数可整合积分算子的几种推广。基于这些新颖的想法，我们推导出一个新颖的框架来研究 $ \breve{C} $eby$ \breve{s} $ev 和 P$ \acute{o} $lya-Szeg$ \ddot{o} $ 类型不等式通过广义 $ \mathcal{K} $-fractional 整合积分运算符。根据广义分数式可适积分理解了几种特殊情况。这种新颖的策略捕获了相关文献中的几个现有结果。我们还旨在展示此处结果与包括 Riemann-Liouville 分数积分算子在内的结果之间的重要联系。