Mathematical modeling of different types of instabilities in time fractional reaction-diffusion systems

In this article we investigate possible scenarios of pattern formations in reaction-diffusion systems with time fractional derivatives. Linear stability analysis is performed for different values of derivative orders. Results of qualitative analysis are confirmed by numerical simulations of specific partial differential equations. Most attention is paid to two models: a fractional order reaction diffusion system with Bonhoeffer–van der Pol kinetics and to the Brusselator model.