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Open AccessFeature PaperArticle
A Factory of Fractional Derivatives
by
Manuel D. Ortigueira
Manuel D. Ortigueira
CTS-UNINOVA and LASI, NOVA School of Science and Technology, NOVA University of Lisbon, 2829-516 Caparica, Portugal
Symmetry 2024, 16(7), 814; https://doi.org/10.3390/sym16070814 (registering DOI)
Submission received: 3 June 2024
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Revised: 19 June 2024
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Accepted: 25 June 2024
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Published: 28 June 2024
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 different paths taken. The 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 obtain both known and new fractional-order derivatives. Several fractional derivatives are considered, mainly Liouville, Hadamard, Euler, bilinear, tempered, q-derivative, and Hahn.
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MDPI and ACS Style
Ortigueira, M.D.
A Factory of Fractional Derivatives. Symmetry 2024, 16, 814.
https://doi.org/10.3390/sym16070814
AMA Style
Ortigueira MD.
A Factory of Fractional Derivatives. Symmetry. 2024; 16(7):814.
https://doi.org/10.3390/sym16070814
Chicago/Turabian Style
Ortigueira, Manuel D.
2024. "A Factory of Fractional Derivatives" Symmetry 16, no. 7: 814.
https://doi.org/10.3390/sym16070814
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