  Many approaches to modelling reaction-diffusion systems with anomalous
transport rely on deterministic equations and ignore fluctuations arising due
to finite particle numbers. Starting from an individual-based model we use a
generating-functional approach to derive a Gaussian approximation for this
intrinsic noise in subdiffusive systems. This results in corrections to the
deterministic fractional reaction-diffusion equations. Using this analytical
approach, we study the onset of noise-driven quasi-patterns in
reaction-subdiffusion systems. We find that subdiffusion can be conducive to
the formation of both deterministic and stochastic patterns. Our analysis shows
that the combination of subdiffusion and intrinsic stochasticity can reduce the
threshold ratio of the effective diffusion coefficients required for pattern
formation to a greater degree than either effect on its own.
