  Dynamical behaviour of discrete dynamical systems has been investigated
extensively in the past few decades. However, in several applications, long
term memory plays an important role in the evolution of dynamical variables.
The definition of discrete maps has recently been extended to fractional maps
to model such situations. We extend this definition to a spatiotemporal system.
We define a coupled map lattice on different topologies, namely,
one-dimensional coupled map lattice, globally coupled system and small-world
network. The spatiotemporal patterns in the fractional system are more ordered.
In particular, synchronization is observed over a large parameter region. For
integer order coupled map lattice in one dimension, synchronized periodic
states with a period greater than one are not obtained. However, we observe
synchronized periodic states with period-3 or period-6 in one dimensional
coupled fractional maps even for a large lattice. With nonlocal coupling, the
synchronization is reached over a larger parameter regime. In all these cases,
the standard deviation decays as power-law in time with the power same as
fractional-order. The physical significance of such studies is also discussed.
