This paper presents a comparison between two nonlinear PID controllers, the first is the Neural based controller and the second is the nonlinear fractional order PID controller (FOPID) for a trajectory tracking control of a non-holonomic two wheeled mobile robots (2-WMR). A modified particle swarm optimization (MPSO) has been proposed in this work to tune the parameters of the nonlinear FOPID controller to design the controller so that the 2-WMR follows exactly a predefined continuous track. The kinematic model of a differential drive 2-WMR has been derived to simulate the behavior of the 2-WMR and it is used in the design and simulations of the proposed FOPID controller. From simulation and results, it can be seen that the efficiency of the proposed nonlinear FOPID controller outperforms the nonlinear integer order PID controller; this is proved by the minimized tracking error and the speed control signals obtained.