During the last years several fractional integrals were investigated. Having this idea in mind, in the present article, some new generalized fractional integral inequalities of the trapezoidal type for ${\lambda }_{\phi }$–preinvex functions, which are differentiable and twice differentiable, are established. Then, by employing those results, we explore the new estimates on trapezoidal type inequalities for classical integral and Riemann–Liouville fractional integrals, respectively. Finally, we apply our new inequalities to construct inequalities involving moments of a continuous random variable.

中文翻译：

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涉及广义分数积分的梯形不等式

在最近几年中，研究了几个分数积分。考虑到这一思想，在本文中，一些新的梯形类型的广义分数积分不等式${\lambda }_{\phi }$–preinvex函数是可微的和两次可微的。然后，利用这些结果，我们分别探索经典积分和Riemann-Liouville分数积分的梯形不等式的新估计。最后，我们应用新的不等式来构造涉及连续随机变量矩的不等式。