In this brief, considering the infinite memory of fractional-order differential equation, a fractional-order echo state network (FESN) is given for time series prediction. For the FESN, the reservoir state differential equation is replaced with fractional-order differential equation. According to the advantages of FESN, the dynamic characteristics of a class of time series can be fully reflected. In order to improve the prediction performance of FESN, a fractional-order output weights learning method and a fractional-order parameter optimization method are given to train the output weights and optimize the reservoir parameters, respectively. Finally, two numerical examples are used to show the effectiveness of FESN.

中文翻译：

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时间序列预测的分数阶回波状态网络

在本文中，考虑到分数阶微分方程的无限存储，给出了分数阶回波状态网络（FESN）用于时间序列预测。对于FESN，用分数阶微分方程代替储层状态微分方程。根据FESN的优点，可以充分反映一类时间序列的动态特性。为了提高FESN的预测性能，分别给出了分数阶输出权重学习方法和分数阶参数优化方法来训练输出权重和优化储层参数。最后，通过两个数值例子说明了FESN的有效性。