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 ae 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. (C) 2000 Elsevier Science B.V. All rights reserved.