基于混合分数阶导数的Lagrange系统Noether对称性研究  

Noether symmetry for Lagrangian system in terms of mixed fractional order derivative

作　　者：宋传静[1] 嵇琳芝 SONG Chuanjing;JI Linzhi(School of Mathematical Sciences,SUST,Suzhou 215009,China)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009

出　　处：《苏州科技大学学报(自然科学版)》2025年第1期19-27,共9页Journal of Suzhou University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金项目(12172241,12272248);江苏高校“青蓝工程”项目。

摘　　要：基于混合分数阶导数研究Lagrange系统的变分问题、对称性与守恒量及对称性的摄动与绝热不变量。这里的混合分数阶导数是经典导数和广义分数阶算子的混合。基于三类混合分数阶导数,首先,建立了系统的运动微分方程;然后,通过研究混合分数阶Hamilton作用量的不变性,建立了Noether恒等式;最后,基于其中的两类混合分数阶导数,研究了系统的守恒量及绝热不变量。The variational problem,symmetry and conserved quantity,as well as perturbation to symmetry and adiabatic invariant are studied for Lagrangian system within mixed fractional order derivative.The mixed fractional order derivative is a mixture of the classical derivative and the generalized fractional order operator.Based on three types of mixed fractional order derivatives,the differential equations of the system were first established.Then,by studying the invariance of the mixed fractional order Hamilton actions,the Noether identities were presented.Finally,based on two types out of the mixed fractional order derivatives,the conserved quantities and adiabatic invariants were explored.

关 键 词：混合分数阶导数 广义分数阶算子 分数阶变分问题 NOETHER对称性 对称性摄动 绝热不变量 

分 类 号：O316[理学—一般力学与力学基础]