Applied Mathematics and Mechanics

, Volume 24, Issue 3, pp 256–260 | Cite as

Applications of fractional exterior differential in three-dimensional space

  • Chen Yong
  • Yan Zhen-ya
  • Zhang Hong-qing


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.

Key words

fractional differential form Cartesian coordinate spherical coordinate cylindrical coordinate 

Chinese Library Classification


2000 MR Subject Classification

26A33 53C26 


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  1. [1]
    Dold A, Eckmann B.Fractional Calculus and Its Aapplications[M]. Berlin: Springer-Verlag, 1975.Google Scholar
  2. [2]
    Kerner R. Z3-graded exterior differential calculus and gauge theories of higher order[J].Lett Math Phys, 1996,36(5):441–454.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Dubois-Violette M. Generalized homologies ford N=0 and graded q-differential algebras [J].Contemp Math, 1998,219(1):69–79.zbMATHMathSciNetGoogle Scholar
  4. [4]
    Coquereaux R. Differentials of higher order in noncommutative differential geometry[J].Lett Math Phys, 1997,42(3):241–259.zbMATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Madore J.An Introduction to Noncommutative Differential Geometry and Its Applications[M]. Cambridge: Cambridge University Press, 1995.Google Scholar
  6. [6]
    Cottrill-Shepherd K, Naber M. Fractional differential forms[J].J Math Phys, 2001,42(5): 2203–2212.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Chen Yong
    • 1
  • Yan Zhen-ya
    • 1
  • Zhang Hong-qing
    • 1
  1. 1.Department of Applied MathematicsDalian University of TechnologyDalianP.R. China

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