基于分数阶导数和变分迭代法的人口预测算法

摘要

An algorithm of population forecast is established by Caputo's fractional derivative,the fractional derivative was extended to modify the Logistic model with harvesting functions,and the variational iteration method is applied to find approximate solutions of the model with Caputo's fractional derivative.As an example of America population forecast,by comparing the Logisticmodel with harvesting function and the model with fractional derivative,the results of this paper are much closer to the actual situation than that obtained by the classical Logistic model.%通过对经典的Logistic模型进行修正,构造一种基于分数阶导数的人口预测算法.主要应用分数阶导数对带有收获函数的Logistic模型进行修正,将经典的Logistic模型修正为分数阶微分模型,再用变分迭代法解修正后的Logistic模型,由此可得到分数阶微分模型的各阶近似解.通过预测美国人口比较了带有收获函数的Logistic模型和分数阶Logistic模型的优缺点.通过比较发现,分数阶Logistic模型能更好的吻合实际数据,提高预测的精度.