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Fractional differential equations of motion in terms of combined Riemann–Liouville derivatives |
Zhang Yi (张毅) |
College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China |
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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.
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Received: 11 December 2011
Revised: 08 January 2012
Accepted manuscript online:
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PACS:
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45.10.Hj
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(Perturbation and fractional calculus methods)
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45.20.Jj
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(Lagrangian and Hamiltonian mechanics)
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02.30.Xx
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(Calculus of variations)
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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
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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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