基于Caputo导数下的含时滞的Hamilton系统的分数阶Noether理论

Fractional Noether theorems for Hamilton system with time delay based on Caputo dervitaves

提出并讨论了Caputo导数定义下的含时滞的Hamilton系统的分数阶Noether对称性与守恒量。根据含时滞的Hamilton系统的分数阶Hamilton原理,建立了相应的含时滞的分数阶Hamilton正则方程;依据分数阶Hamilton作用量在无限小变换下的不变性,得到了含时滞的Hamilton系统的分数阶Noether对称性;最后,建立了系统的含时滞的分数阶Noether理论,并举例说明结果的应用。

The fractional Noether symmetries and fractional conserved quantities for Hamilton system with time delay based on Caputo derivatives are discussed.The fractional Hamilton canonical equations of the corresconding system with time delay are established base upon the fractional Hamilton principle of the Hamilton systems with time delay.Then,the fractional Noether symmetries of the Hamilton system with time delay are obtained,which based on the invariance of the fractional Hamilton action with time delay under the infinitesimal transformations of group.Finally,fractional Noether theorems with time delay of the Hamilton system are established.At the end,one example is given to illustrate the application of the results.