  With the discovery of new superconductors there was a running to find the
justifications for the new properties found in these materials. In order to
describe these new effects some theories were adapted and some others have been
tried. In this work we present an application of the fractional calculus to
study the superconductor in the context of London theory. Here we investigated
the linear London equation modified by fractional derivatives for
non-differentiable functions, instead of integer ones, in a coarse grained
scenario. We apply the fractional approach based in the modified
Riemann-Liouville sense to improve the model in order to include possible
non-local interactions and the media. It is argued that the e ects of
non-locality and long memory, intrinsic to the formalism of the fractional
calculus, are relevant to achieving a satisfactory phenomenological
description. In order to compare the present results with the usual London
theory, we calculated the magnetic field distribution for a mesoscopic
superconductor system. Also, a fractional Pippard-like model is proposed to
take into account the non-locality beside effects of interactions and the
media. We propose that parameter alfa of fractionality can be used to create an
alternative way to characterize superconductors.
