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Discrete-Time Fractional Difference Calculus: Origins, Evolutions, and New Formalisms
Version 1
: Received: 9 May 2023 / Approved: 10 May 2023 / Online: 10 May 2023 (10:15:22 CEST)
A peer-reviewed article of this Preprint also exists.
Ortigueira, M.D. Discrete-Time Fractional Difference Calculus: Origins, Evolutions, and New Formalisms. Fractal Fract. 2023, 7, 502. Ortigueira, M.D. Discrete-Time Fractional Difference Calculus: Origins, Evolutions, and New Formalisms. Fractal Fract. 2023, 7, 502.
Abstract
Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time are described. ARMA type systems based on differencers are introduced and exemplified. In passing, the incorrectness of the usual delta difference is shown.
Keywords
nabla difference; delta difference; ARMA; ARFIMA; bilateral difference; tempered; bilinear; stretching difference
Subject
Engineering, Other
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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