A novel three-step iterative approach for oscillatory chemical reactions of fractional brusselator model

In this paper, we present a three-step iterative approach for solving the fractional Brusselator model. The fractional derivatives are described in the Caputo, Caputo-Fabrizio, and Atangana-Baleanu senses. The fractional differential equation is converted into an analogous integral equation and then obtained using the three-step iterative approach. The method consists of first implementing the trapezoidal rule and then performing the iteration approach on the resulting equation. In the fractional Brusselator model, we examine the stability of equilibrium points. For each fractional order operator, simulations were performed and analyzed in order to verify the method's high feasibility and efficiency, as well as to confirm the theoretical aspect. The obtained solution simulations suggest that the methodology utilised is robust, time-efficient, and appropriate for dealing with the system of fractional equations of small fractional order from a numerical standpoint.