Based on the pseudo-order relation, we introduce the concept of left and right $\hslash$-preinvex interval-valued functions (LR-$\hslash$-PIVFs). Further, we establish the Hermite–Hadamard and Hermite–Hadamard–Fejér-type estimates for LR-$\hslash$-PIVFs using generalized fractional integrals. Finally, an example of interval-valued fractional integrals is provided to illustrate the validity of the results derived herein. Our results not only extend some existing inequalities for Hadamard, Riemann–Liouville, and Katugampola fractional integrals, but also provide new insights for future research on generalized convexity and IVFs, among others.

基于伪序关系，我们引入了左、右 $\hslash$ -前倒数区间值函数（LR- $\hslash$ -PIVF）的概念。此外，我们使用广义分数积分建立了 LR- $\hslash$ -PIVF 的 Hermite-Hadamard 和 Hermite-Hadamard-Fejér 型估计。最后，提供了一个区间值分数积分的例子来说明本文得出的结果的有效性。我们的结果不仅扩展了 Hadamard、Riemann-Liouville 和 Katugampola 分数积分的一些现有不等式，而且还为广义凸性和 IVF 等的未来研究提供了新的见解。