快速检索:      
引用本文:
【打印本页】   【下载PDF全文】   查看/发表评论  【EndNote】   【RefMan】   【BibTex】
←前一篇|后一篇→ 过刊浏览    高级检索
本文已被:浏览 89次   下载 218 本文二维码信息
码上扫一扫!
分享到: 微信 更多
四阶时间分数阶演化方程的Lie对称分析和守恒律
王丽,田守富,冯连莉,宋晓秋
作者单位E-mail
王丽 中国矿业大学 数学学院, 徐州 221116  
田守富 中国矿业大学 数学学院, 徐州 221116 sftian@cumt.edu.cn,shoufu2006@126.com 
冯连莉 中国矿业大学 数学学院, 徐州 221116 songxiaoqiu@cumt.edu.cn 
宋晓秋 中国矿业大学 数学学院, 徐州 221116  
摘要:
主要研究了四阶时间分数阶演化方程的Lie对称分析和守恒.基于Lie点对称方法,分别得到了该方程的相关向量场以及相似约化.在相似约化的基础上,通过该方法来获得分数阶常微分方程是非常有效的.最后,通过非线性的自伴随方法和时间分数阶的黎曼-刘维尔导数算子以及欧拉-拉格朗日算子,得到了该方程的守恒律.
关键词:  Lie对称方法  对称分析  守恒律
DOI:10.3969/J.ISSN.100-5137.2017.03.004
分类号:
基金项目:This research was supported by the National Training Programs of Innovation and Entrepreneurship for Undergraduates (201410290039);the Fundamental Research Funds for the Central Universities (2015QNA53, 2015XKQY14);the General Financial Grant from the China Postdoctoral Science Foundations (2015M570498 and 2017T100413);Natural Sciences Foundation of China (11301527)
Lie symmetry analysis and conservation laws for the time fractional fourth-order evolution equation
Wang Li,Tian Shoufu,Feng Lianli,Song Xiaoqiu
Abstract:
In this paper, we study Lie symmetry analysis and conservation laws for the time fractional nonlinear fourth-order evolution equation. Using the method of Lie point symmetry, we provide the associated vector fields, and derive the similarity reductions of the equation, respectively. The method can be applied wisely and efficiently to get the reduced fractional ordinary differential equations based on the similarity reductions. Finally, by using the nonlinear self-adjointness method and Riemann-Liouville time-fractional derivative operator as well as Euler-Lagrange operator, the conservation laws of the equation are obtained.
Key words:  Lie symmetry method  symmetry analysis  conservation laws