Fractional central differences and derivatives

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Fractional central differences and derivatives are studied in this article. These are generalisations to real orders of the ordinary positive (even and odd) integer order differences and derivatives, and also coincide with the well known Riesz potentials. The coherence of these definitions is studied by applying the definitions to functions with Fourier transformable functions. Some properties of these derivatives are presented and particular cases studied.

Original languageEnglish
Pages (from-to)1255-1266
Number of pages12
JournalJournal of Vibration and Control
Issue number9-10
Publication statusPublished - Sep 2008


  • Fractional central derivative
  • Fractional central difference
  • Generalized Cauchy derivative
  • Grnwald-Letnikov


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