含Caputo型分数阶导数的灰色预测模型

针对缺乏统计规律的小样本预测系统,如何挖掘其发展规律,一直是学术界的难点.本文依据分数阶微积分理论,将整数阶导数灰色模型推广到分数阶导数灰色模型,并从是否满足新信息优先原理、初值利用情况、还原误差大小和稳定性等方面说明了新模型的优势,以期用Caputo型分数阶导数的记忆性描述小样本预测系统.实例表明含有Caputo型分数阶导数的灰色预测模型的有效性与实用性.

Grey model with Caputo fractional order derivative

How to make use of the law in forecasting system with small sample and lack of statistics properties is a problem. The integer order derivative of grey prediction model is extended to fractional order derivative based on fractional calculus in order to use the memory property of fractional order derivative to describe the forecasting system with small sample, and we prove that grey prediction model with fractional order derivative is better than that of grey prediction model with integer order derivative for principle of new information priority, effect of initial value, stability and so on. The effectiveness and practicability of the proposed model are validated by a real example.