  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.
