基于按周期律拓展的El-Nabulsi分数阶模型的Birkhoff系统的积分因子方法  

Application of integrating factor method to Birkhoff system based on El-Nabulsi fractional integral model extended by periodic law

作　　者：蔡琼辉 朱建青[1] CAI Qionghui;ZHU Jianqing(School of Mathematics and Physics,SUST,Suzhou 215009,China)

机构地区：[1]苏州科技大学数理学院,江苏苏州215009

出　　处：《苏州科技大学学报（自然科学版）》2019年第1期11-15,共5页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11572212);苏州科技大学研究生科研创新计划资助项目(SKYCX16_010)

摘　　要：为了进一步研究积分因子方法理论在分数阶模型中的应用,将积分因子方法应用于基于按周期律拓展的Birkhoff系统,建立了寻找基于按周期律拓展的Birkhoff系统守恒量的一种新方法。首先,给出基于按周期律拓展的分数阶El-Nabulsi-Birkhoff方程,并定义出方程的积分因子;其次,详细地研究了守恒量存在的必要条件,同时找出积分因子与守恒量之间的关系,得出了广义Killing方程,建立相应的守恒定理;最后,通过举例来说明结果的应用。In order to further study the application of integrating factor method in fractional order model,we applied it to the Birkhoff system extended by periodic law and proposed a new method for finding the conserved quantities of the Birkhoff system. Firstly,the fractional order El-Nabulsi-Birkhoff equation extended by periodic law was given,and the integrating factor of equation was defined. Secondly,the necessary conditions for the existence of conserved quantities were studied,and the relationship between the integral factor and the conserved quantity was explored. A generalized Killing equation was obtained,and the corresponding conservation theorem was established. Finally,an example was given to illustrate the application of the results.

关 键 词：按周期律拓展的分数阶积分 El-Nabulsi-Birkhoff方程 积分因子 守恒量 

分 类 号：O316[理学—一般力学与力学基础]