Fractional cyclic integrals and Routh equations of fractional Lagrange system with combined Caputo derivatives

doi:10.1088/1674-1056/23/12/124501

›› 2014, Vol. 23 ›› Issue (12): 124501-124501.doi: 10.1088/1674-1056/23/12/124501

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Fractional cyclic integrals and Routh equations of fractional Lagrange system with combined Caputo derivatives

王琳莉, 傅景礼

Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China

收稿日期:2014-04-10 修回日期:2014-05-26 出版日期:2014-12-15 发布日期:2014-12-15
基金资助:
Project supported by the National Natural Science Foundations of China (Grant Nos. 11272287 and 11472247) and the Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT) (Grant No. IRT13097).

Fractional cyclic integrals and Routh equations of fractional Lagrange system with combined Caputo derivatives

Wang Lin-Li (王琳莉), Fu Jing-Li (傅景礼)

Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China

Received:2014-04-10 Revised:2014-05-26 Online:2014-12-15 Published:2014-12-15
Contact: Fu Jing-Li E-mail:sqfujingli@163.com
Supported by:
Project supported by the National Natural Science Foundations of China (Grant Nos. 11272287 and 11472247) and the Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT) (Grant No. IRT13097).

摘要/Abstract

摘要： In this paper, we develop a fractional cyclic integral and a Routh equation for fractional Lagrange system defined in terms of fractional Caputo derivatives. The fractional Hamilton principle and the fractional Lagrange equations of the system are obtained under a combined Caputo derivative. Furthermore, the fractional cyclic integrals based on the Lagrange equations are studied and the associated Routh equations of the system are presented. Finally, two examples are given to show the applications of the results.

关键词: fractional cyclic integral, fractional Routh equation, combined Caputo fractional derivative

Abstract: In this paper, we develop a fractional cyclic integral and a Routh equation for fractional Lagrange system defined in terms of fractional Caputo derivatives. The fractional Hamilton principle and the fractional Lagrange equations of the system are obtained under a combined Caputo derivative. Furthermore, the fractional cyclic integrals based on the Lagrange equations are studied and the associated Routh equations of the system are presented. Finally, two examples are given to show the applications of the results.

Key words: fractional cyclic integral, fractional Routh equation, combined Caputo fractional derivative

中图分类号: (Perturbation and fractional calculus methods)

45.10.Hj

02.30.Xx (Calculus of variations) 45.20.Jj (Lagrangian and Hamiltonian mechanics)

王琳莉, 傅景礼. Fractional cyclic integrals and Routh equations of fractional Lagrange system with combined Caputo derivatives[J]. , 2014, 23(12): 124501-124501.

Wang Lin-Li (王琳莉), Fu Jing-Li (傅景礼). Fractional cyclic integrals and Routh equations of fractional Lagrange system with combined Caputo derivatives[J]. Chin. Phys. B, 2014, 23(12): 124501-124501.

参考文献 0


[1]	Podlubny I 1999 Fractional Differential Equations (San Diego CA: Academic Press)

[2]	Miller K S and Ross B 1993 An Introduction to the Fractional Calculus and Fractional Differential Equations (New York: John Wiley & Sons, Inc.)

[3]	Hilf R 2000 Applications of Fractional Calculus in Physics (Singapore: World Scientific Publishing Company)

[4]	Samko S G, Kilbas A A and Marichev O I 1993 Fractional Integrals and Derivatives——Theory and Applications (Linghorne, PA: Gordon and Breach)

[5]	Kilbas A A, Srivastava H M and Trujillo J J 2006 Theory and Applications of Fractional Differential Equations (Amsterdam: Elsevier B V)

[6]	Tarasov V E 2010 Fractional Dynamics (Beijing: Higher Education Press)

[7]	Oldham K B and Spanier J 1974 The Fractional Calculus (New York: Academic Press)

[8]	Zaslavsky G M 2005 Hamiltonian Chaos and Fractional Dynamics (Oxford: Oxford University Press)

[9]	Zaslavsky G M and Edelman M A 2004 Physica D 193 128 doi: 10.1016/j.physd.2004.01.014

[10]	Riewe F 1996 Phys. Rev. E 53 1890 doi: 10.1103/PhysRevE.53.1890

[11]	Riewe F 1997 Phys. Rev. E 55 3581 doi: 10.1103/PhysRevE.55.3581

[12]	Agrawal O P 2002 J. Math. Anal. Appl. 272 368 doi: 10.1016/S0022-247X(02)00180-4

[13]	Zhou S, Fu J L and Liu Y S 2010 Chin. Phys. B 19 120301

[14]	Zhang Y 2012 Chin. Phys. B 21 084502

[15]	Baleanu D and Agrawal O P 2006 Czechoslovak J. Phys. 56 1087 doi: 10.1007/s10582-006-0406-x

[16]	Malinowska A B and Torres D F M 2010 "Fractional Variational Calculus in Terms of a Combined Caputo Derivative", in: Proceedings of 4th IFAC Workshop on Fractional Derivative and Application. Article No. FDA10-084

Fractional cyclic integrals and Routh equations of fractional Lagrange system with combined Caputo derivatives

Fractional cyclic integrals and Routh equations of fractional Lagrange system with combined Caputo derivatives

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