On the Fractional Derivative Duality in Some Transforms-Reference-Cited by-同舟云学术

On the Fractional Derivative Duality in Some Transforms

Published:2023-10-27 Issue:21 Volume:11 Page:4464
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Ortigueira Manuel Duarte¹^ORCID,Bengochea Gabriel²^ORCID

Affiliation:

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

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.

Funder

Foundation for Science and Technology of Portugal

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/21/4464/pdf

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4. Poularikas, A.D. (1999). Handbook of Formulas and Tables for Signal Processing, CRC Press.

5. Bracewell, R.N. (2000). The Fourier Transform and Its Applications, McGraw-Hil Higher Education.