In this paper, we propose a new fractional operator which is based on the weight function for Atangana–Baleanu [Formula: see text]-fractional operators. A motivating characteristic is the generalization of classical variants within the weighted [Formula: see text]-fractional integral. We aim to establish Minkowski and reverse Hölder inequalities by employing weighted [Formula: see text]-fractional integral. The consequences demonstrate that the obtained technique is well-organized and appropriate.

中文翻译：

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加权非奇异分数积分算子意义上的新泛化

在本文中，我们提出了一种新的分数算子，它基于 Atangana-Baleanu [公式：见正文]-分数算子的权重函数。一个激励特征是在加权[公式：见正文]-分数积分中的经典变体的推广。我们的目标是通过使用加权 [公式：见文本]-分数积分来建立 Minkowski 和反转 Hölder 不等式。结果表明，所获得的技术是组织良好和适当的。