The present article deals with the new estimates in the view of generalized proportional fractional integral with respect to another function. In the present investigation, we focus on driving certain new classes of integral inequalities utilizing a family of positive functions $ n(n\in\mathbb{N}) $ for this newly defined operator. From the computed outcomes, we concluded some new variants for classical generalized proportional fractional and other integrals as remarks. These variants are connected with some existing results in the literature. Certain interesting consequent results of the main theorems are also pointed out.

中文翻译：

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一些新的边界类似于相对于另一个函数的广义比例分数积分算子

本文从相对于另一个函数的广义比例分数积分的角度处理新的估计。在目前的调查中，我们专注于利用一系列正函数 $ n(n\in\mathbb{N}) $ 为这个新定义的运算符驱动某些新的积分不等式。从计算结果中，我们总结了经典广义比例分数和其他积分的一些新变体作为备注。这些变体与文献中的一些现有结果有关。还指出了主要定理的某些有趣的后续结果。