包含时间分数阶导数与整数阶导数的一类微分方程Lie对称

Lie Symmetry of a Class of Differential Equations Involving Time Fractional Derivative and Integer Derivative

摘要: 针对同时含有时间整数阶导数和Caputo分数阶导数的一类常微分方程，采用Lie对称理论，给出了该分数阶微分方程的Lie对称分类。据我们所知，研究分数阶导数Lie对称的人们主要考虑包含时间分数阶导数和空间变量的整数阶导数的微分方程。为此，本文中，通过Caputo分数阶的相关性质Caputo分数阶微分方程的Lie理论，给出了所考虑的微分方程拥有的对称定理，对部分情况给出了原方程的Lie对称约化。

Abstract: For a class of ordinary differential equations containing both time integer derivative and Caputo fractional derivative, the Lie symmetry classification of the fractional differential equations is given by using the Lie symmetry theory. As far as we know, people who study fractional derivative Lie symmetry mainly consider differential equations that include fractional derivatives of time and in-teger derivatives of spatial variables. Therefore, in this paper, the symmetry theorem of the differ-ential equation under consideration is given through the Lie theory of Caputo fractional order dif-ferential equation, and the Lie symmetry reduction of the original equation is given for some cases.