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

Stochastic fluctuations and quasi-pattern formation in reaction-diffusion systems with anomalous transport