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On the fractional derivative duality in some transforms
Version 1
: Received: 4 October 2023 / Approved: 4 October 2023 / Online: 9 October 2023 (15:13:50 CEST)
A peer-reviewed article of this Preprint also exists.
Ortigueira, M.D.; Bengochea, G. On the Fractional Derivative Duality in Some Transforms. Mathematics 2023, 11, 4464. Ortigueira, M.D.; Bengochea, G. On the Fractional Derivative Duality in Some Transforms. Mathematics 2023, 11, 4464.
Abstract
The duality is one of the most interesting properties of the Laplace and Fourier transforms associated to 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.
Keywords
Liouville derivative; scale derivative; Hadamard derivative; Laplace transform; Mellin transform; Z transform; Fourier transform
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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