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In this paper, we consider a time-fractional reaction-diffusion system withthe same nonlinearities of the Newton-Leipnik chaotic system. Throughanalytical tools and numerical results, we derive sufficient conditions for theasymptotic stability of the proposed model and show the existence of chaos. Wealso propose a nonlinear synchronization controller for a pair of systems andestablish the local and global asymptotic convergence of the trajectories bymeans of fractional stability theory and the Lyapunov method.

On the complete synchronization of a time-fractional reaction-diffusion system with the Newton-Leipnik nonlinearity