How Many Fractional Derivatives Are There?

How Many Fractional Derivatives Are There?

In this paper, we introduce a unified fractional derivative, defined by two parameters (order and asymmetry). From this, all the interesting derivatives can be obtained. We study the one-sided derivatives and show that most known derivatives are particular cases. We consider also some myths of Fract...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 10; no. 5; p. 737
Main Authors: Valério, Duarte, Ortigueira, Manuel D., Lopes, António M.
Format: Journal Article
Language:English
Published: Basel MDPI AG 01-03-2022
Subjects:
Engineering
Fourier transforms
Fractional calculus
fractional derivative
Mathematics
signals and systems
Online Access:Get full text
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Summary:In this paper, we introduce a unified fractional derivative, defined by two parameters (order and asymmetry). From this, all the interesting derivatives can be obtained. We study the one-sided derivatives and show that most known derivatives are particular cases. We consider also some myths of Fractional Calculus and false fractional derivatives. The results are expected to contribute to limit the appearance of derivatives that differ from existing ones just because they are defined on distinct domains, and to prevent the ambiguous use of the concept of fractional derivative.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10050737