基于Riemann-Liouville导数的分数阶Pfaff-Birkhoff原理和分数阶Birkhoff方程  

Fractional Pfaff-Birkhoff Principle and Fractional Birkhoff's Equations in Terms of Riemann-Liouville Derivatives

作　　者：周燕[1] 张毅[2] 

机构地区：[1]苏州科技学院数理学院,江苏215009 [2]苏州科技学院土木工程学院,江苏215009

出　　处：《科技通报》2013年第3期4-10,共7页Bulletin of Science and Technology

基　　金：国家自然科学基金(10972151;11272227);江苏省普通高校研究生科研创新计划(CXZZ11_0949);苏州科技学院研究生科研创新计划(SKCX11S_050)资助项目

摘　　要：研究分数阶Pfaff-Birkhoff变分问题。列写出Riemann-Liouville分数阶导数的定义及其有关性质。建立了基于Riemann-Liuville分数阶导数的分数阶Pfaff-Birkhoff原理,并由分数阶Pfaff-Birkhoff原理推导出了分数阶Birkhoff方程及其横截性条件。研究表明:整数阶Pfaff-Birkhoff原理和Birkhoff方程是本文结果的特例。文末举例说明结果的应用。The fractional Pfaff-Birkhoff variational problem is studied in this paper.The definition of Riemann-Liouville fractional derivatives and some of their properties are listed.The fractional Pfaff-Birkhoff principle is established in terms of Riemann-Liouville fractional derivatives,then the fractional Birkhoff＇s equations and the corresponding transversality conditions are derived.The research shows： the traditional Pfaff-Birkhoff principle and Birkhoff＇s equations are special cases of our results.Finally an example is given to illustrate the application of the results.

关 键 词：Riemann-Liouville分数阶导数 分数阶Pfaff-Birkhoff原理 分数阶Birkhoff方程 横截性条件 

分 类 号：O316[理学—一般力学与力学基础]