A sigmoidal fractional derivative for regularization

In this paper, we propose a new fractional derivative, which is based on a Caputo-type derivative with a smooth kernel. We show that the proposed fractional derivative reduces to the classical derivative and has a smoothing effect which is compatible with $\ell_{1}$ regularization. Moreover, it sati...

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Bibliographic Details
Published inAIMS mathematics Vol. 5; no. 4; pp. 3284 - 3297
Main Authors Rezapour, Mostafa, Sijuwade, Adebowale, Asaki, Thomas
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
caputo derivative
fractional calculus
regularization
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Summary:In this paper, we propose a new fractional derivative, which is based on a Caputo-type derivative with a smooth kernel. We show that the proposed fractional derivative reduces to the classical derivative and has a smoothing effect which is compatible with $\ell_{1}$ regularization. Moreover, it satisfies some classical properties.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020211