Propagation in Fisher-KPP type equations with fractional diffusion in   periodic media
  We are interested in the time asymptotic location of the level sets of solutions to Fisher-KPP reaction-diffusion equations with fractional diffusion in periodic media. We show that the speed of propagation is exponential in time, with a precise exponent depending on a periodic principal eigenvalue, and that it does not depend on the space direction. This is in contrast with the Freidlin-G\"artner formula for the standard Laplacian. 
Xavier Cabre, Anne-Charline Coulon, Jean-Michel Roquejoffre
math.AP