Pattern formation mechanisms in one-dimensional Brusselator with fractional derivatives

The paper summarizes results on the formation of nontrivial space-time patterns in two component medium with anomalous diffusion and nonlinear reaction kinetics. It is shown that such medium might be formalized as systems of fractional differential equations. Two model problems — superdiffusion with the same order of fractional derivatives and subdiffusion of mixed order — are studied by means of linear theory. Analytical derivations are accompanied by the series of numerical experiments.