On the Fractional Derivative Duality in Some Transforms

Manuel Duarte Ortigueira, Gabriel Bengochea

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Abstract

Duality is one of the most interesting properties of the Laplace and Fourier transforms associated with the integer-order derivative. Here, we will generalize it for fractional derivatives and extend the results to the Mellin, Z and discrete-time Fourier transforms. The scale and nabla derivatives are used. Some consequences are described.
Original languageEnglish
Article number4464
Number of pages15
JournalMathematics
Volume11
Issue number21
DOIs
Publication statusPublished - 27 Oct 2023

Keywords

  • Fourier transform
  • Hadamard derivative
  • Laplace transform
  • Liouville derivative
  • Mellin transform
  • scale derivative
  • Z transform

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