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Self-organization phenomena in reaction–diffusion systems with non-integer order time derivatives

This paper considers a one-dimensional fractional reaction–diffusion model with a different order of derivative indices. The corresponding linear stability analysis is presented for any number of fractional derivative indices that are greater than zero but less than two. It was shown that instability can arise for the Hopf and the Turing modes. The self-organization phenomena are more diverse when the activator derivative index is greater than the inhibitor one than when the inhibitor variable index is greater. This analysis was supported by the results of computer simulations of the fractional nonlinear reaction–diffusion problem.