Bruce Henry Department of Applied Mathematics, University of New South Wales Fractional Reaction-Diffusion Equations and Pattern Formation Wednesday 8th, March 14:05-14:55pm, Carslaw Building Room 373. One of the best understood models for spatial pattern formation in physical and biological systems is based on Turing instability analysis of reaction-diffusion equations where reactions obey the law of mass action and diffusion is standard Brownian motion. In recent years there have been numerous experimental reports of anomalous diffusion in which the mean square displacement of diffusing species scales as a nonlinear power of time. Indeed there is growing evidence that anomalous diffusion is ubiquitous in biological systems. In this talk I will describe the attempts of our group to extend Turing instability analysis to model pattern formation in fractional reaction-diffusion equations where fractional order temporal derivatives are used to model the anomalous diffusion. Our results demonstrate that Turing instability analysis of these systems provides a reliable indicator of both the onset and the nature of the patterns that form, including the possibility of complex spatio-temporal patterns that do not occur in standard reaction-diffusion models. The elements of Turing pattern formation, continuous time random walks, and fractional calculus will be introduced at a level appropriate to an audience that is not familiar with these topics.