AIMS Mathematics, 2020, 5(4): 3284-3297. doi: 10.3934/math.2020211.

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A sigmoidal fractional derivative for regularization

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

The first two authors contributed equally to this work.

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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Keywords fractional calculus; Caputo derivative; regularization

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

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