| 四阶时间分数阶演化方程的Lie对称分析和守恒律 |
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| 引用本文： | 王丽,田守富,冯连莉,宋晓秋.四阶时间分数阶演化方程的Lie对称分析和守恒律[J].上海师范大学学报(自然科学版),2017,46(3):363-374. |
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| 作者姓名： | 王丽 田守富 冯连莉 宋晓秋 |
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| 作者单位： | 中国矿业大学 数学学院, 徐州 221116,中国矿业大学 数学学院, 徐州 221116,中国矿业大学 数学学院, 徐州 221116,中国矿业大学 数学学院, 徐州 221116 |
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| 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) |
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| 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.
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| 关 键 词： | Lie对称方法 对称分析 守恒律 |
| 收稿时间： | 2016/9/12 0:00:00 |
Lie symmetry analysis and conservation laws for the time fractional fourth-order evolution equation |
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| Wang Li,Tian Shoufu,Feng Lianli and Song Xiaoqiu.Lie symmetry analysis and conservation laws for the time fractional fourth-order evolution equation[J].Journal of Shanghai Normal University(Natural Sciences),2017,46(3):363-374. |
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| Authors: | Wang Li Tian Shoufu Feng Lianli and Song Xiaoqiu |
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| Institution: | School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China,School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China,School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China and School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China |
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| 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. |
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| Keywords: | Lie symmetry method symmetry analysis conservation laws |
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