In the article, we present several generalizations for the generalized Čebyšev type inequality in the frame of quantum fractional Hahn’s integral operator by using the quantum shift operator . As applications, we provide some associated variants to illustrate the efficiency of quantum Hahn’s integral operator and compare our obtained results and proposed technique with the previously known results and existing technique. Our ideas and approaches may lead to new directions in fractional quantum calculus theory.

中文翻译：

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关于量子哈恩积分算子对分数阶微积分的新修改

在本文中，我们使用量子位移算子对量子分数Hahn积分算子框架中的广义Čebyšev型不等式进行了几种推广 。作为应用，我们提供一些相关的变体来说明量子哈恩积分算子的效率，并将我们获得的结果和提出的技术与先前已知的结果和现有技术进行比较。我们的思想和方法可能会为分数量子微积分理论带来新的方向。