## 留言板

 引用本文: 陈勇, 闫振亚, 张鸿庆. 分数外微分在三维空间中的应用[J]. 应用数学和力学, 2003, 24(3): 229-233.
CHEN Yong, YAN Zhen-ya, ZHANG Hong-qing. Applications of Fractional Exterior Differential in Three-Dimensional Space[J]. Applied Mathematics and Mechanics, 2003, 24(3): 229-233.
 Citation: CHEN Yong, YAN Zhen-ya, ZHANG Hong-qing. Applications of Fractional Exterior Differential in Three-Dimensional Space[J]. Applied Mathematics and Mechanics, 2003, 24(3): 229-233.

• 中图分类号: O175

## Applications of Fractional Exterior Differential in Three-Dimensional Space

• 摘要: 首先介绍了分数微积分和分数微分形式。讨论了在原点处对曲线坐标的分数外微分变换,并且获得了从三维卡氏坐标到球面坐标和柱面坐标的两个分数微分变换。特别地,当v=m=1时,这两个分数微分变换约化的结果与通过外微积分获得的结果是一致的。
•  [1] Dold A,Eckmann B.Fractional Calculus and Its Aapplications[M].Berlin:Springer-Verlag,1975. [2] Kerner R.Z3-graded exterior differential calculus and gauge theories of higher order[J].Lett Math Phys,1996,36(5):441-454. [3] Dubois-Violette M.Generalized homologies for dN=0 and graded q-differential algebras[J].Contemp Math,1998,219(1):69-79. [4] Coquereaux R.Differentials of higher order in noncommutative differential geometry[J].Lett Math Phys,1997,42(3):241-259. [5] Modore J.An Introduction to Noncommutative Differential Geometry and Its Applications[M].Cambridge:Cambridge University Press,1995. [6] Cottrill-Shepherd K,Naber M.Fractional differential forms[J].J Math Phys,2001,42(5):2203-2212.

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##### 出版历程
• 收稿日期:  2001-10-09
• 修回日期:  2002-06-08
• 刊出日期:  2003-03-15

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