Fractional derivatives and integrations of non-integers orders was introduced
more than three centuries ago but only recently gained more attention due to
its application on nonlocal phenomenas. In this context, several formulations
of fractional electromagnetic fields was proposed, but all these theories
suffer from the absence of an effective fractional vector calculus, and in
general are non-causal or spatially asymmetric. In order to deal with these
difficulties, we propose a spatially symmetric and causal gauge invariant
fractional electromagnetic field from a Lagrangian formulation. From our
fractional Maxwell's fields arose a definition for the fractional gradient,
divergent and curl operators.Comment: accepted for publication in Physics Letters
