In this paper we introduce a novel extension of sampling operators by replacing the sample values \((f(k/w))_{k=0}^{n}\) with its fractional average (mean) value in n-dimensional parallelepiped. Using the Riemann–Liouville fractional integral operator of order \(\alpha \), we define fractional type multivariate sampling operators based upon a suitable kernel function. Moreover, we give convergence results for these operators in \(C(\mathbf{R}^n)\) and Orlicz spaces and obtain multivariate Voronovskaya type asymptotic formula by means of Euler-Beta functions. Finally, several graphical and numerical results are presented to demonstrate the accuracy, applicability and efficiency of the operators through special kernels.

在本文中，我们通过将样本值\((f(k/w))_{k=0}^{n}\)替换为其n维的分数平均值（均值）来引入采样算子的新扩展平行六面体。使用\(\alpha \)阶的黎曼-刘维尔分数积分算子，我们根据合适的核函数定义分数类型多元采样算子。此外，我们给出了这些算子在\(C(\mathbf{R}^n)\)和Orlicz 空间中的收敛结果，并通过Euler-Beta 函数得到了多元Voronovskaya 型渐近公式。最后，给出了几个图形和数值结果，以通过特殊内核证明算子的准确性、适用性和效率。