Turing instability in the Lengyel–Epstein fractional Laplacian system

This paper discusses a space-fractional version of the conventional Lengyel–Epstein CIMA reaction model. First, we prove the global existence, uniqueness, and boundedness of a unique solution. We next investigate the system fundamental analytic properties. Following this, we establish the conditions on the reactor size and diffusion coefficient such that the system does not allow positive steady-state solutions that are not constant. Finally, the stability of constant steady-state solutions for ODE and PDE models is studied.