A new sigmoidal fractional derivative for regularization

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.

References in corpus (5)

• Fractional Calculus: Integral and Differential Equations of Fractional Order
• No Nonlocality. No Fractional Derivative
• A New Fractional Derivative with Classical Properties
• Convolutional neural networks with fractional order gradient method
• Convolution based smooth approximations to the absolute value function with application to non-smooth regularization