Chaotic dynamical systems are studied in this paper. In the models, integer order time derivatives are replaced with the Caputo fractional order counterparts. A Chebyshev spectral method is presented for the numerical approximation. In each of the systems considered, linear stability analysis is established. A range of chaotic behaviours are obtained at the instances of fractional power which show the evolution of the species in time and space.
Keywords: chaotic dynamics; chebyshev spectral method; fractional differential equation; spatiotemporal oscillations; stability analysis.