Propagation in a fractional reaction-diffusion equation in a periodically hostile environment

Abstract: We provide an asymptotic analysis of a fractional Fisher-KPP type equation in periodic non-connected 1-dimensional media with Dirichlet conditions outside the domain. After demonstrating the existence and uniqueness of a non-trivial bounded stationary state $n_+$ , we prove that the stable state $n_+$ invades the unstable state 0 with a speed which is exponential in time.