  In this paper, we consider a time-fractional reaction-diffusion system with
the same nonlinearities of the Newton-Leipnik chaotic system. Through
analytical tools and numerical results, we derive sufficient conditions for the
asymptotic stability of the proposed model and show the existence of chaos. We
also propose a nonlinear synchronization controller for a pair of systems and
establish the local and global asymptotic convergence of the trajectories by
means of fractional stability theory and the Lyapunov method.
