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On the Fractional Derivative Duality in Some Transforms

Author

Listed:
  • 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)

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.

Suggested Citation

  • Manuel Duarte Ortigueira & Gabriel Bengochea, 2023. "On the Fractional Derivative Duality in Some Transforms," Mathematics, MDPI, vol. 11(21), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4464-:d:1269201
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