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We provide an asymptotic analysis of a fractional Fisher-KPP type equation inperiodic non-connected 1-dimensional media with Dirichlet conditions outsidethe domain. After demonstrating the existence and uniqueness of a non-trivialbounded stationary state $n\_+$ , we prove that the stable state $n\_+$ invadesthe unstable state 0 with a speed which is exponential in time.

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