  Adopting a particular approach to fractional calculus, this paper sets out to
build up a consistent extension of the Faddeev-Jackiw (or Symplectic) algorithm
to carry out the quantization procedure of coarse-grained models in the
standard canonical way. In our treatment, we shall work with the Modified
Riemman Liouville (MRL) approach for fractional derivatives, where the chain
rule is as efficient as it is in the standard differential calculus. We still
present a case where we consider the situation of charged particles moving on a
plane with velocity $\dot{r}$, subject to an external and intense magnetic
field in a coarse-grained scenario. We propose an interesting parallelism with
the noncommutative case.
