This paper proves an equality for the case of differentiable convex functions including the conformable fractional integrals. By using this equality, we establish several parameterized inequalities with the help of the conformable fractional integrals. Several inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Furthermore, we present previously achieved results and new results by using special cases of the obtained theorems.

中文翻译：

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对一致分数积分参数化不等式的广泛研究

本文证明了包含适形分数积分的可微凸函数情况的等式。通过使用这个等式，我们借助一致分数积分建立了几个参数化不等式。利用凸性、Hölder 不等式和幂均不等式可以得到几个不等式。此外，我们通过使用所获得定理的特殊情况来展示先前取得的结果和新结果。