A new sigmoidal fractional derivative for regularization

TL;DR

This paper introduces a novel fractional derivative based on a Caputo-type derivative with a smooth kernel, which generalizes classical derivatives and enhances regularization techniques.

Contribution

The paper presents a new fractional derivative that combines smooth kernel properties with classical derivative compatibility, improving regularization methods.

Findings

Reduces to classical derivative under certain conditions

Provides smoothing effect compatible with  regularization

Satisfies classical properties of derivatives

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.