A sigmoidal fractional derivative for regularization

Mostafa Rezapour; Adebowale Sijuwade; Thomas Asaki; Mostafa Rezapour; Adebowale Sijuwade; Thomas Asaki

doi:10.3934/math.2020211

AIMS Mathematics

2020, Volume 5, Issue 4: 3284-3297. doi: 10.3934/math.2020211

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Research article

A sigmoidal fractional derivative for regularization

Department of Mathematics and Statistics, Washington State University, Pullman, WA, USA

Received: 16 January 2020 Accepted: 26 March 2020 Published: 30 March 2020
MSC : 26A33

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.
- fractional calculus,
- Caputo derivative,
- regularization
Citation: Mostafa Rezapour, Adebowale Sijuwade, Thomas Asaki. A sigmoidal fractional derivative for regularization[J]. AIMS Mathematics, 2020, 5(4): 3284-3297. doi: 10.3934/math.2020211

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Abstract

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.

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