Effects of Fractional Derivative on Stability and Pattern Formation in a Time-Fractional Reaction–Diffusion Model

This paper investigates a time-fractional reaction–diffusion system, and develops an efficient numerical method for the system. The fractional orders serve as key bifurcation parameters, capable of inducing instabilities and rich pattern structures. We analyze and and simulate the stability conditions, bifurcation behavior, and pattern formation mechanisms of the system, and explore how variations in the fractional orders modulate the underlying dynamics.