Fractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues that impose a number of computational constraints. In this talk we discuss efficient, scalable techniques for solving fractional-in-space reaction diffusion equations combining the finite element method with robust techniques for computing the fractional power of a matrix times a vector. We shall demonstrate the methods on a number examples which show the qualitative difference in solution profiles between standard and fractional diffusion models.
