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Volume 11
Issue 21
10.3390/math11214464
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Article

On the Fractional Derivative Duality in Some Transforms

by
Manuel Duarte Ortigueira
1,* and
Gabriel Bengochea
2
1
NOVA School of Science and Technology, UNINOVA-CTS and LASI, NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal
2
Academia de Matemáticas, Universidad Autónoma de la Ciudad de México, Prolongación San Isidro 151, Col. San Lorenzo Tezonco, Del. Iztapalapa, Ciudad de México C.P. 09790, Mexico
*
Author to whom correspondence should be addressed.
Mathematics 2023, 11(21), 4464; https://doi.org/10.3390/math11214464
Submission received: 3 October 2023 / Revised: 23 October 2023 / Accepted: 24 October 2023 / Published: 27 October 2023
(This article belongs to the Special Issue Recent Research on Fractional Calculus: Theory and Applications)
Versions Notes

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

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MDPI and ACS Style

Ortigueira, M.D.; Bengochea, G. On the Fractional Derivative Duality in Some Transforms. Mathematics 2023, 11, 4464. https://doi.org/10.3390/math11214464

AMA Style

Ortigueira MD, Bengochea G. On the Fractional Derivative Duality in Some Transforms. Mathematics. 2023; 11(21):4464. https://doi.org/10.3390/math11214464

Chicago/Turabian Style

Ortigueira, Manuel Duarte, and Gabriel Bengochea. 2023. "On the Fractional Derivative Duality in Some Transforms" Mathematics 11, no. 21: 4464. https://doi.org/10.3390/math11214464

APA Style

Ortigueira, M. D., & Bengochea, G. (2023). On the Fractional Derivative Duality in Some Transforms. Mathematics, 11(21), 4464. https://doi.org/10.3390/math11214464

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