Abstract
Linear stability theory is developed for an activator–inhibitor model where fractional derivative operators of generally different exponents act both on diffusion and reaction terms. It is shown that in the short wave limit the growth rate is a power law of the wave number with decoupled time scales for distinct anomaly exponents of the different species. With equal anomaly exponents an exact formula for the anomalous critical value of reactants diffusion coefficients' ratio is obtained.
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