| Fractional differential equations of motion in terms of combined Riemann—Liouville derivatives |
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| 引用本文： | 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. |
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| 作者姓名： | 张毅 |
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| 作者单位： | College of Civil Engineering,Suzhou University of Science and Technology |
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| 基金项目： | Project supported by the National Natural Science Foundation of China （Grant No. 10972151）. |
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| 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.
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| 关 键 词： | fractional Hamilton principle fractional Lagrange equation fractional Hamilton canonical equation combined Riemann-Liouville fractional derivative |
| 收稿时间： | 2011-12-11 |
Fractional differential equations of motion in terms of combined Riemann-Liouville derivatives |
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| Zhang Yi.Fractional differential equations of motion in terms of combined Riemann-Liouville derivatives[J].Chinese Physics B,2012,21(8):84502-084502. |
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| Authors: | Zhang Yi |
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| Institution: | 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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| Keywords: | fractional Hamilton principle fractional Lagrange equation fractional Hamilton canonical equation combined Riemann-Liouville fractional derivative |
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