Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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