Fractional differential equations of motion in terms of combined Riemann–Liouville derivatives

doi:10.1088/1674-1056/21/8/084502

Abstract In this paper, we focus on studying the fractional variational principle and the differential equations of motion for a fractional mechanical system. A combined Riemann-Liouville fractional derivative operator is defined, and a fractional Hamilton principle under this definition is established. The fractional Lagrange equations and the fractional Hamilton canonical equations are derived from the fractional Hamilton principle. A number of special cases are given, showing the universality of our conclusions. At the end of the paper, an example is given to illustrate the application of the results.

Keywords: fractional Hamilton principle fractional Lagrange equation fractional Hamilton canonical equation combined Riemann-Liouville fractional derivative

Received: 11 December 2011
Revised: 08 January 2012
Accepted manuscript online:

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

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10972151).

Corresponding Authors: Zhang Yi
E-mail: weidiezh@pub.sz.jsinfo.net

Cite this article:

Zhang Yi (张毅) Fractional differential equations of motion in terms of combined Riemann–Liouville derivatives 2012 Chin. Phys. B 21 084502

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Fractional differential equations of motion in terms of combined Riemann–Liouville derivatives

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