arXiv subjects
Publications and source records attributed to Adebowale Sijuwade.
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.
In this paper, we present a new derivative via the Laplace transform. The Laplace transform leads to a natural form of the fractional derivative which is equivalent to a Riemann-Liouville derivative with fixed terminal point. We first consider a representation which interacts well with periodic functions, examine some rudimentary properties and propose a generalization. The interest for this new approach arose from recent developments in fractional differential equations involving Caputo-type derivatives and applications in regularization problems.