Solitary travelling auto-waves in fractional reaction–diffusion systems

Abstract In this article we study properties of solitary auto-waves in nonlinear fractional reaction–diffusion systems. As an example, the generalised FitzHugh–Nagumo model with time-fractional derivatives is considered. By a linear stability analysis and computer simulation it is shown that the order of the fractional derivative can substantially change the properties of solitary auto-waves and significantly enrich nonlinear system dynamics. The main properties of solitary travelling wave solutions, including the shape of the waves, the domain of their existence, as well as the parameters of their propagation in fractional reaction–diffusion systems, are investigated.