分数外微分在三维空间中的应用

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基金项目: 国家自然科学基金资助项目(10072013);重点基础研究发展规划项目(G1998030600)

Applications of Fractional Exterior Differential in Three-Dimensional Space

Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China

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。
- 分数微分形式 /
- 卡氏坐标 /
- 球面坐标 /
- 柱面坐标
Abstract: A brief survey of fractional calculus and fractional differential forms was firstly given.The fractional exterior transition to curvilinear coordinate at the origin were discussed and the two coordinate transformations for the fractional differentials for three-dimensional Cartesian coordinates to spherical and cylindrical coordinates are obtained, respectively.In particular, for v=m=1, the usual exterior transformations, between the spherical coordinate and Cartesian coordinate, as well as the cylindrical coordinate and Cartesian coordinate, are found respectively, from fractional exterior transformation.
- fractional differential form /
- Cartesian coordinate /
- spherical coordinate /
- cylindrical coordinate

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