分数因子与分数阶完整力学系统的运动方程和循环积分
Fractional Motion Equations and Circulatory Integrals of Holonomic Dynamical Systems with Fractional Gene
查看参考文献31篇
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文摘
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引入分数因子和分数增量,给出了分数阶微积分的定义和性质;基于分数阶导数的定义,证明了含有分数因子的等时变分与分数阶算子的交换关系;提出了分数阶完整保守和非保守系统的Hamilton原理;建立了分数阶完整保守系统和非保守系统的运动微分方程;得到了分数阶完整保守系统的循环积分;并利用分数阶循环积分导出分数阶罗兹方程.最后给出了两个例子.研究表明利用分数因子给出的分数阶微分方程是一个含有分数因子的通常的微分方程,那么分数阶系统运动微分方程的求解都可以采用通常微分方程的求解方法. |
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其他语种文摘
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Firstly, a fractional gene and a fractional increment are put forward and the definitions and properties of fractional derivative and integral with fractional gene are given. Secondly, the exchanging relationship between the isochronous variation and fractional derivative with the fractional gene is proved. Thirdly, the fractional Hamilton principles and fractional differential equations with fractional gene for holonomic dynamical systems are presented. Further, the fractional circulatory integrals of the systems are obtained and the fractional Routh's equations with fractional gene are derived. Finally, two examples are given. This research indicates that the fractional differential equations can become the conventional differential equations with fractional gene, and the general methods for solving the conventional differential equations are also applicable for solving the fractional differential equations. |
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来源
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力学季刊
,2016,37(2):252-265 【扩展库】
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DOI
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10.15959/j.cnki.0254-0053.2016.02.006
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关键词
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分数因子
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循环积分
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罗兹方程
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分数阶完整力学系统
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地址
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浙江理工大学数学物理研究所, 浙江, 杭州, 310018
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语种
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中文 |
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文献类型
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研究性论文 |
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ISSN
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0254-0053 |
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学科
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力学 |
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基金
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国家自然科学基金
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国家教育部长江学者与创新团队发展计划
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文献收藏号
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CSCD:5744161
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参考文献 共
31
共2页
|
|
1.
Hilfer R.
Applications of fractional calculus in physics,2000
|
CSCD被引
113
次
|
|
|
|
|
2.
寇磊. 分数阶微分型双参数黏弹性地基矩形板受荷响应.
力学季刊,2013,34(1):154-160
|
CSCD被引
6
次
|
|
|
|
|
3.
刘林超. 简谐荷载作用下分数导数粘弹性土体中圆形隧道洞的应力位移分析.
力学季刊,2012,33(1):85-90
|
CSCD被引
2
次
|
|
|
|
|
4.
朱克勤. 粘弹性流体的分数元模型及圆管起动流.
力学季刊,2007,28(4):521-527
|
CSCD被引
2
次
|
|
|
|
|
5.
许震宇. 纤维加强复合材料的总体粘弹性响应.
力学季刊,2003,24(2):191-197
|
CSCD被引
1
次
|
|
|
|
|
6.
Gorenflo R. Random walk models for space-fractional diffusion processes.
Fractional Calculus and Applied Analysis,1998,1:167-191
|
CSCD被引
11
次
|
|
|
|
|
7.
Tadjeran C. A second-order accurate numerical approximation for the fractional diffusion equation.
Journal of Computational Physics,2006,213(1):205-213
|
CSCD被引
18
次
|
|
|
|
|
8.
Krepysheva N. Fractional diffusion and reflective boundary condition.
Physica A,2006,368:355-361
|
CSCD被引
1
次
|
|
|
|
|
9.
Gorenflo R. Continuous-time random walk and parametric subordination in fractional diffusion.
Chaos Solitons and Fractals,2007,34:87-103
|
CSCD被引
2
次
|
|
|
|
|
10.
Henry B I. Fractional reaction-diffusion.
Physica A,2000,276:448-455
|
CSCD被引
9
次
|
|
|
|
|
11.
Rocco A. Fractional calculus and the evolution of fractal phenomena.
Physica A,1999,265:535-546
|
CSCD被引
3
次
|
|
|
|
|
12.
Carpinteri A. A fractional calculus approach to the description of stress and strain localization in fractal media.
Chaos Solitons and Fractals,2002,13:85-94
|
CSCD被引
7
次
|
|
|
|
|
13.
Yao K. On the connection between the order of fractional calculus and the dimensions of a fractal function.
Chaos Solitons and Fractals,2005,23:621-629
|
CSCD被引
7
次
|
|
|
|
|
14.
Yao K. The relationship between the fractal dimensions of a type of fractal functions the order of their fractional calculus.
Chaos Solitons and Fractals,2007,34:682-692
|
CSCD被引
1
次
|
|
|
|
|
15.
Mainardi F. Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
Chaos Solitons and Fractals,1996,7:1461-1477
|
CSCD被引
24
次
|
|
|
|
|
16.
Ryabov Y E. Damped oscillation in view of the fractional oscillator equation.
Physical Review B,2002,66:184-201
|
CSCD被引
2
次
|
|
|
|
|
17.
Tofighi A. The intrinsic damping of the fractional oscillator.
Physica A,2003,329:29-34
|
CSCD被引
4
次
|
|
|
|
|
18.
王在华. 含分数阶导数阻尼的线性振动系统的稳定性.
中国科学G辑:物理学、力学、天文学,2009,39(10):1495-1502
|
CSCD被引
16
次
|
|
|
|
|
19.
Baleanu D. Fractional Hamilton formalism within Caputo's derivative.
Czechoslovak Journal of Physics,2006,56:1087-1092
|
CSCD被引
10
次
|
|
|
|
|
20.
Zhou S. Lagrange equations of nonholonomic systems with fractional derivatives.
Chinese Physics B,2010,19:120301
|
CSCD被引
12
次
|
|
|
|
|
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