一种基于阶次转换的分数阶微分方程近似解法  

An Approximate Solution of Fractional Differential Equation Based on Order Conversion

作　　者：郑志静 王璐[1,2] ZHENG Zhijing;WANG Lu(Department of General Education, Chengdu Neusoft University, Chengdu 611844;Geomathematics Key Laboratory of Sichuan Province, Chengdu University of Technology, Chengdu 610059 China)

机构地区：[1]成都东软学院基础教学部,四川成都611844 [2]成都理工大学数学地质四川省重点实验室,四川成都610059

出　　处：《湘潭大学自然科学学报》2017年第4期10-13,共4页Natural Science Journal of Xiangtan University

基　　金：数学地质四川省重点实验室开放基金项目(scsxdz201610);数学地质四川省重点实验室开放基金项目(scsxdz2013004)

摘　　要：基于Caputo分数微分和Riemann-Liouville分数微分的理论,通过阶次转换,将高阶分数阶微分方程转换成经典的整数阶微分方程,继而进行近似求解.数值实验结果表明了该方法的有效性.Based on the theory of Caputo fractional derivative and Riemann Liouville fractional derivative theory,the higher order fractional differential equation is transformed into classical integer differential equation by order transformation,then the approximate solution is obtained.The numerical results show that this method is valid.

关 键 词：分数阶微分方程 高阶分数阶 阶次转换 Caputo微分 RiemannLiouville微分 

分 类 号：O241[理学—计算数学]