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

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

中国物理B ›› 2012, Vol. 21 ›› Issue (8): 84502-084502.doi: 10.1088/1674-1056/21/8/084502

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

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

张毅

College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

收稿日期:2011-12-11 修回日期:2012-01-08 出版日期:2012-07-01 发布日期:2012-07-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10972151).

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

Received:2011-12-11 Revised:2012-01-08 Online:2012-07-01 Published:2012-07-01
Contact: Zhang Yi E-mail:weidiezh@pub.sz.jsinfo.net
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10972151).

摘要/Abstract

摘要： 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.

关键词: fractional Hamilton principle, fractional Lagrange equation, fractional Hamilton canonical equation, combined Riemann-Liouville fractional derivative

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.

Key words: fractional Hamilton principle, fractional Lagrange equation, fractional Hamilton canonical equation, combined Riemann-Liouville fractional derivative

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

45.10.Hj

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

张毅. Fractional differential equations of motion in terms of combined Riemann–Liouville derivatives[J]. 中国物理B, 2012, 21(8): 84502-084502.

Zhang Yi (张毅). Fractional differential equations of motion in terms of combined Riemann–Liouville derivatives[J]. Chin. Phys. B, 2012, 21(8): 84502-084502.

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

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

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