This work mainly investigates a class of convex interval-valued functions via the Katugampola fractional integral operator. By considering the p-convexity of the interval-valued functions, we establish some integral inequalities of the Hermite–Hadamard type and Hermite–Hadamard–Fejér type as well as some product inequalities via the Katugampola fractional integral operator. In addition, we compare our results with the results given in the literature. Applications of the main results are illustrated by using examples. These results may open a new avenue for modeling, optimization problems, and fuzzy interval-valued functions that involve both discrete and continuous variables at the same time.

这项工作主要是通过Katugampola分数积分算子研究一类凸间隔值函数。通过考虑区间值函数的p凸性，我们建立了Hermite–Hadamard型和Hermite–Hadamard–Fejér型的一些积分不等式，以及通过Katugampola分数阶积分算子的某些乘积不等式。另外，我们将我们的结果与文献中给出的结果进行比较。通过举例说明主要结果的应用。这些结果可能会为建模，优化问题和同时包含离散变量和连续变量的模糊区间值函数开辟新的途径。