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

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

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.

Keywords: fractional cyclic integral fractional Routh equation combined Caputo fractional derivative

Received: 10 April 2014
Revised: 26 May 2014
Accepted manuscript online:

PACS:	45.10.Hj	(Perturbation and fractional calculus methods)
	02.30.Xx	(Calculus of variations)
	45.20.Jj	(Lagrangian and Hamiltonian mechanics)

Fund: 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).

Corresponding Authors: Fu Jing-Li
E-mail: sqfujingli@163.com

Cite this article:

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 2014 Chin. Phys. B 23 124501


[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

[10]	Riewe F 1996 Phys. Rev. E 53 1890

[11]	Riewe F 1997 Phys. Rev. E 55 3581

[12]	Agrawal O P 2002 J. Math. Anal. Appl. 272 368

[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

[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

[1]	Transient transition behaviors of fractional-order simplest chaotic circuit with bi-stable locally-active memristor and its ARM-based implementation Zong-Li Yang(杨宗立), Dong Liang(梁栋), Da-Wei Ding(丁大为), Yong-Bing Hu(胡永兵), and Hao Li(李浩). Chin. Phys. B, 2021, 30(12): 120515.
[2]	The (3+1)-dimensional generalized mKdV-ZK equation for ion-acoustic waves in quantum plasmas as well as its non-resonant multiwave solution Xiang-Wen Cheng(程香雯), Zong-Guo Zhang(张宗国), and Hong-Wei Yang(杨红卫). Chin. Phys. B, 2020, 29(12): 124501.
[3]	Conserved quantities and adiabatic invariants of fractional Birkhoffian system of Herglotz type Juan-Juan Ding(丁娟娟), Yi Zhang(张毅). Chin. Phys. B, 2020, 29(4): 044501.
[4]	Primary resonance of fractional-order Duffing-van der Pol oscillator by harmonic balance method Sujuan Li(李素娟), Jiangchuan Niu(牛江川), Xianghong Li(李向红). Chin. Phys. B, 2018, 27(12): 120502.
[5]	Non-Noether symmetries of Hamiltonian systems withconformable fractional derivatives Lin-Li Wang (王琳莉) and Jing-Li Fu(傅景礼). Chin. Phys. B, 2016, 25(1): 014501.
[6]	Time fractional dual-phase-lag heat conduction equation Xu Huan-Ying (续焕英), Jiang Xiao-Yun (蒋晓芸). Chin. Phys. B, 2015, 24(3): 034401.
[7]	Noether's theorems of a fractional Birkhoffian system within Riemann–Liouville derivatives Zhou Yan (周燕), Zhang Yi (张毅). Chin. Phys. B, 2014, 23(12): 124502.
[8]	Lie symmetry theorem of fractional nonholonomic systems Sun Yi (孙毅), Chen Ben-Yong (陈本永), Fu Jing-Li (傅景礼). Chin. Phys. B, 2014, 23(11): 110201.
[9]	Effects of switching frequency and leakage inductance on slow-scale stability in a voltage controlled flyback converter Wang Fa-Qiang (王发强), Ma Xi-Kui (马西奎). Chin. Phys. B, 2013, 22(12): 120504.
[10]	Transfer function modeling and analysis of the open-loop Buck converter using the fractional calculus Wang Fa-Qiang (王发强), Ma Xi-Kui (马西奎). Chin. Phys. B, 2013, 22(3): 030506.
[11]	Variational iteration method for solving the time-fractional diffusion equations in porous medium Wu Guo-Cheng (吴国成). Chin. Phys. B, 2012, 21(12): 120504.
[12]	Modeling and dynamics analysis of the fractional-order Buck–Boost converter in continuous conduction mode Yang Ning-Ning (杨宁宁), Liu Chong-Xin (刘崇新), Wu Chao-Jun (吴朝俊 ). Chin. Phys. B, 2012, 21(8): 080503.
[13]	Fractional differential equations of motion in terms of combined Riemann–Liouville derivatives Zhang Yi (张毅). Chin. Phys. B, 2012, 21(8): 084502.
[14]	Period-doubling bifurcation in two-stage power factor correction converters using the method of incremental harmonic balance and Floquet theory Wang Fa-Qiang(王发强), Zhang Hao (张浩), and Ma Xi-Kui(马西奎) . Chin. Phys. B, 2012, 21(2): 020505.
[15]	Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems Luo Shao-Kai(罗绍凯), Chen Xiang-Wei(陈向炜), and Guo Yong-Xin(郭永新). Chin. Phys. B, 2007, 16(11): 3176-3181.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention