Fractional Noether's Theorems for El-Nabulsi's Fractional Birkhoffian Systems in Terms of Riemann-Liouville Derivatives  

作　　者：宋传静 张毅 

机构地区：[1]College of Science, Nanjing University of Science and Technology, Nanjing 210094, China [2]College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

出　　处：《Journal of Donghua University(English Edition)》2017年第1期14-20,共7页东华大学学报（英文版）

基　　金：National Natural Science Foundations of China(Nos.11572212,11272227,10972151);the Innovation Program for Scientific Research of Nanjing University of Science and Technology,China;the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province,China(No.KYLX15_0405)

摘　　要：The fractional Pfaffian variational problem and Noether’s theorems were investigated in terms of Riemann-Liouville derivatives on the basis of El-Nabulsi fractional model.The problem of the calculus of variations with fractional derivatives is a hot topic recently.Firstly,within Riemann-Liouville derivatives,the ElNabulsi Pfaffian variational problem was presented,the fractional Pfaff-Birkhoff-d’Alembert principle was established,and the fractional Birkhoff equations and the corresponding transversality conditions were obtained.Then,the Noether’s theorems in terms of Riemann-Liouville derivatives for the Birkhoffian system on the basis of El-Nabulsi fractional model are investigated under the special and the general transformations respectively.Finally,an example is given to illustrate the methods and results appeared in this paper.The fractional Pfaffian variational problem and Noether＇s theorems were investigated in terms of Riemann-Liouville derivatives on the basis of EI-Nabulsi fractional model. The problem of the calculus of variations with fractional derivatives is a hot topic recently. Firstly, within Riemann-Liouville derivatives, the E1- Nabulsi Pfaffian variational problem was presented, the fractional Pfaff-Birkhoff-d＇Alembert principle was established, and the fractional Birkhoff equations and the corresponding transversality conditions were obtained. Then, the Noether＇s theorems in terms of Riemann-Liouville derivatives for the Birkhoffian system on the basis of EI-Nabulsi fractional model are investigated under the special and the general transformations respectively. Finally, an example is given to illustrate the methods and results appeared in this paper.

关 键 词：fractional Birkhoff equations transversality condition calculus of variations fractional derivatives Noether’s theorem 

分 类 号：O316[理学—一般力学与力学基础]