四阶时间分数阶演化方程的Lie对称分析和守恒律

摘要

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 RiemannLiouville time-fractional derivative operator as well as Euler-Lagrange operator,the conservation laws of the equation are obtained.%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.