A new Laplace-type fractional derivative
General Mathematics
2020-02-03 v5
Abstract
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.
Cite
@article{arxiv.1912.12810,
title = {A new Laplace-type fractional derivative},
author = {Mostafa Rezapour and Adebowale Sijuwade},
journal= {arXiv preprint arXiv:1912.12810},
year = {2020}
}