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Chin. Phys. B, 2012, Vol. 21(8): 084502    DOI: 10.1088/1674-1056/21/8/084502
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

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
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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