On the Fractional Derivative Duality in Some Transforms

Manuel Duarte Ortigueira () and Gabriel Bengochea
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Manuel Duarte Ortigueira: NOVA School of Science and Technology, UNINOVA-CTS and LASI, NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal
Gabriel Bengochea: 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

Mathematics, 2023, vol. 11, issue 21, 1-15

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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