Article
Version 1
Preserved in Portico This version is not peer-reviewed
A Factory of Fractional Derivatives
Version 1
: Received: 4 June 2024 / Approved: 5 June 2024 / Online: 5 June 2024 (15:24:22 CEST)
A peer-reviewed article of this Preprint also exists.
Ortigueira, M.D. A Factory of Fractional Derivatives. Symmetry 2024, 16, 814. Ortigueira, M.D. A Factory of Fractional Derivatives. Symmetry 2024, 16, 814.
Abstract
This paper aims to demonstrate that, beyond the small world of Riemann-Liouville and Caputo derivatives, there is a vast and rich world with many derivatives suitable for specific problems and various theoretical frameworks to develop, corresponding to the different paths taken. Notions of time and scale sequences are introduced and general associated basic derivatives, namely right/stretching and left/shrinking, are defined. A general framework for fractional derivative definitions is reviewed and applied to get both known and new fractional order derivatives. Several fractional derivatives are considered, mainly: Liouville, Hadamard, Euler, bilinear, tempered, q-derivative, and Hahn.
Keywords
Shift-invariant; Scale-invariant; Nabla derivative; Fractional q-derivative; Fractional Hahn derivative.
Subject
Computer Science and Mathematics, Analysis
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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