一类分数阶微分方程的李对称分析和守恒定律

Lie Symmetry Analysis and Conservation Laws of a Class of Fractional Differential Equations

利用李对称方法研究一类分数阶微分方程的约化和守恒定律.根据给出的方程李对称分析,得到无穷小生成元,求解出方程的精确解.通过相似变换与相似变量,将方程约化为带有Erdélyi-Kober分数阶算子的非线性常微分方程.进一步在李代数的基础上,讨论分数阶微分方程的守恒定律,并分别求得x分量和t分量的守恒向量.

The reduction and conservation law of a class of fractional differential equations are solved by the Lie symmetry analysis.According to the Lie symmetry analysis of the given equation,we can get the infinitesi.mal generator,and find out the exact solution of the system.Then,the equation is reduced to a nonlinear ordi.nary differential equation with Erdélyi-Kober fractional operator through similarity transformation and similar.ity variables.And,on the basis of Lie algebra,the conservation law of fractional differential equation is dis.cussed,and the conservation vector of x and t components is given respectively.