Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional(2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction–diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor. Stability formations in an Oregonator model with superdiffusion are studied in two-dimensional (2D) numerical simulations. Stability analyzes are performed by applying Fourier and Laplace transforms to the space fractional reaction-diffusion systems. Antispiral, stable turing patterns, and traveling patterns are observed by changing the diffusion index of the activator. Analyzes of Floliers multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the traveling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor.