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Unexpected behavior of Caputo fractional derivative

descriptionPublicationkeyboard_double_arrow_right Article 03 Feb 2016 Brazil English Publisher:Springer Science and Business Media LLCJournal:Computational and Applied Mathematics, volume 36, pages 1,173-1,183 (issn: 0101-8205, eissn: 1807-0302, Copyright policy )
Authors: Kuroda, Lucas Kenjy Bazaglia; Gomes, Arianne Vellasco; Tavoni, Robinson; de Arruda Mancera, Paulo Fernando; Varalta, Najla; de Figueiredo Camargo, Rubens;

doi: 10.1007/s40314-015-0301-9

handle: 11449/175076

Unexpected behavior of Caputo fractional derivative

Abstract

This paper discusses the modeling via mathematical methods based on fractional calculus, using Caputo fractional derivative. From the fractional models associated with harmonic oscillator, logistic equation and Malthusian growth, an unexpected behavior of the Caputo fractional derivative is discussed. The difference between the rate of variation and the order of the Caputo fractional derivative is explained.

Country
Brazil
Related Organizations
Keywords

Caputo fractional derivative, Fractional modeling, Fractional calculus, Fractional logistic equation, Fractional harmonic oscillator

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    		 20
    popularity
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    		 Top 10%
    influence
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
20
Top 10%
Top 10%
Top 10%
Green
bronze