Fractional reaction–diffusion

We derive a fractional reaction–diffusion equation from a continuous-time random walk model with temporal memory and sources. The equation provides a general model for reaction–diffusion phenomena with anomalous diffusion such as occurs in spatially inhomogeneous environments. As a first investigation of this equation we consider the special case of single species fractional reaction–diffusion in one dimension and show that the fractional diffusion does not by itself precipitate a Turing instability.