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Applications of fractional exterior differential in three-dimensional space

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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.

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Authors and Affiliations

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

    Chen Yong Doctor, Yan Zhen-ya & Zhang Hong-qing

Authors
  1. Chen Yong Doctor
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  2. Yan Zhen-ya
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  3. Zhang Hong-qing
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Additional information

Contributed by Zhang Hong-qing

Foundation items: the National Natural Science Foundation of China (10072013); the National Key Basic Research Development Project Program of China (G1998030600)

Biography: Chen Yong (1960-)

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Yong, C., Zhen-ya, Y. & Hong-qing, Z. Applications of fractional exterior differential in three-dimensional space. Appl Math Mech 24, 256–260 (2003). https://doi.org/10.1007/BF02438263

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  • DOI: https://doi.org/10.1007/BF02438263

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