One-dimensional Brusselator with time-fractional derivative

In the present paper possible scenarios of pattern formation in non-linear media with diffusion and differential operators of non-integer order are studied for the abstract Brusselator model. By means of the standard linear analysis exact critical values for different types of instabilities are derived. It is shown that stability criteria significantly depend on the order of the fractional derivative in case of the Hopf and C2TH bifurcations. Predictions of the linear theory are confirmed by numerical simulation. The exposition is accompanied by a concise survey of the main results in the fields of fractional calculus and dynamical systems of non-integer order.