Based on the idea of fractional calculus, reverse accumulated generating operators of real number’s order are proposed in this paper. We claim the set of these operators forms a 1-dimensional additive real Lie group, which is isomorphic to $\mathbb{R}$. As a direct consequence, the weakening buffer operators of positive real number’s order are constructed. Compared with traditional weakening buffer operators of integer number’s order, this formulation could make finer adjustments on weight distributions between original data sequence by varying the order of weakening buffer operators, which can take a balance between the influence of disturbance components and the tracking speed of parameter estimation. Applications of this construction are used in GM $(1,1)$ model and multiple linear regression models, experimental results show that the proposed buffer operator can effectively improve the prediction accuracy.

基于分数演算的思想，提出了实数阶逆累积生成算子。我们声称这些算子的集合构成一维加法实李群，与 $\mathbb{[R}$。直接的结果就是构造了正实数阶的弱化缓冲算子。与传统的整数阶弱化缓冲算子相比，通过改变弱化缓冲算子的阶数，该公式可以对原始数据序列之间的权重分布进行更好的调整，从而可以在干扰分量的影响和参数的跟踪速度之间取得平衡。估计。通用汽车使用了这种结构的应用 $（\mathrm{1个}，\mathrm{1个}）$ 实验模型和多元线性回归模型的实验结果表明，所提出的缓冲算子可以有效提高预测精度。