We derive a fractional reaction-diffusion equation from a continuous-time r
andom walk model with temporal memory and sources. The equation provides a
general model for reaction-diffusion phenomena with anomalous diffusion suc
h as occurs in spatially inhomogeneous environments. As a first investigati
on of this equation ae consider the special case of single species fraction
al reaction-diffusion in one dimension and show that the fractional diffusi
on does not by itself precipitate a Turing instability. (C) 2000 Elsevier S
cience B.V. All rights reserved.