In this paper, we establish certain generalized fractional integral inequalities of mean and trapezoid type for $(s+1)$ -convex functions involving the $(k,s)$ -Riemann–Liouville integrals. Moreover, we develop such integral inequalities for h-convex functions involving the k-conformable fractional integrals. The legitimacy of the derived results is demonstrated by plotting graphs. As applications of the derived inequalities, we obtain the classical Hermite–Hadamard and trapezoid inequalities.

中文翻译：

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应用不同凸度的某些均值型分数积分不等式及其应用

在本文中，我们为涉及（$ k，s）$ -Riemann–Liouville积分的$（s + 1）$-凸函数建立了均值和梯形类型的某些广义分数积分不等式。此外，我们为涉及k可整合分数分数的h凸函数开发了此类积分不等式。通过绘制图形可以证明得出的结果的合法性。作为导出不等式的应用，我们获得了经典的Hermite-Hadamard和梯形不等式。