On Fractional-Order Discrete-Time Reaction Diffusion Systems

Reaction–diffusion systems have a broad variety of applications, particularly in biology, and it is well known that fractional calculus has been successfully used with this type system. However, analyzing these using discrete novel requires significant research diversity disciplines. Thus, paper, we investigate the discrete-time fractional-order Lengyel–Epstein system as model chlorite iodide malonic acid (CIMA) chemical reaction. With help second order difference operator, describe model. Furthermore, linearization approach, established acceptable requirements for local asymptotic stability system’s unique equilibrium. Moreover, employ Lyapunov functional to show when feeding rate moderate, constant equilibrium solution globally asymptotically stable. Finally, numerical models are presented validate theoretical conclusions demonstrate impact discretization on dynamics. The continuous version reaction–diffusion compared under consideration.