We study a generalized left sided tempered fractional (GTF)-integral concerning another function Ψ in the kernel. Then we investigate several kinds of inequalities such as Grüss-type and certain other related inequalities by utilizing the GTF-integral. Additionally, we present various special cases of the main result. By utilizing the connection between GTF-integral and Riemann–Liouville integral concerning another function Ψ in the kernel, certain distinct particular cases of the main result are also presented. Furthermore, certain other inequalities can be formed by applying various kinds of conditions on the function Ψ.

中文翻译：

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关于其他函数的回火分数积分的某些Grüss型不等式

我们研究了关于内核中另一个函数general的广义左侧回火分数（GTF）-积分。然后，我们利用GTF积分研究了几种不等式，例如Grüss型不等式和某些其他相关不等式。此外，我们介绍了主要结果的各种特殊情况。通过利用GTF积分与Riemann-Liouville积分之间有关内核中另一个函数the的联系，还给出了主要结果的某些不同的特殊情况。此外，可以通过对函数various施加各种条件来形成某些其他不等式。