On the Fractional Derivative Duality in Some Transforms

Manuel Duarte Ortigueira; Gabriel Bengochea

doi:10.3390/math11214464

On the Fractional Derivative Duality in Some Transforms

Manuel Duarte Ortigueira, Gabriel Bengochea

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4 Citations (Scopus)

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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 language	English
Article number	4464
Number of pages	15
Journal	Mathematics
Volume	11
Issue number	21
DOIs	https://doi.org/10.3390/math11214464
Publication status	Published - 27 Oct 2023

Keywords

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

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10.3390/math11214464Licence: CC BY

On the Fractional Derivative DualityFinal published version, 307 KBLicence: CC BY

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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.",

keywords = "Fourier transform, Hadamard derivative, Laplace transform, Liouville derivative, Mellin transform, scale derivative, Z transform",

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N2 - 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.

AB - 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.

KW - Fourier transform

KW - Hadamard derivative

KW - Laplace transform

KW - Liouville derivative

KW - Mellin transform

KW - scale derivative

KW - Z transform

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On the Fractional Derivative Duality in Some Transforms

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Keywords

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