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.