On the Fractional Derivative Duality in Some Transforms

Ortigueira, Manuel DuarteBengochea, Gabriel2024-02-222024-02-222023-10-27PURE: 83890871PURE UUID: 1218d30c-7e26-4235-9c5f-0bffefcd7855Scopus: 85176559003WOS: 001100418700001ORCID: /0000-0003-4270-3284/work/153838372http://hdl.handle.net/10362/163980The first author was partially funded by national funds through the Foundation for Science and Technology of Portugal under the projects UIDB/00066/2020. Publisher Copyright: © 2023 by the authors.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.15314622engFourier transformHadamard derivativeLaplace transformLiouville derivativeMellin transformscale derivativeZ transformComputer Science (miscellaneous)General MathematicsEngineering (miscellaneous)On the Fractional Derivative Duality in Some Transformsjournal article10.3390/math11214464https://www.scopus.com/pages/publications/85176559003