Improve Solutions of Non‐Linear Fractional Belovsov‐Zhbotinsky System Using Particle Swarm Optimization With He's Polynomial

ABSTRACT

Polynomials are used to solve many types of nonlinear and fractional equations and systems that represent various situations in nature, including chemical systems that exhibit periodic, nonlinear behavior, such as the nonlinear fractional Belousov‐Zhabotinsky system. These polynomials produce a term series that describes the system's behavior and highlights its nonlinearity. From these polynomials, He's polynomial was used to find a term series that reflects the periodic and nonlinear behavior of the system under different initial conditions. To enhance the accuracy of the study of the behavior of the chemical system, the particle swarm optimization (PSO) algorithm was used to detect the influence of system parameters during the solution. This algorithm yielded very high accuracy in the parameter selection process, facilitating the understanding of periodic stability and characteristic transitions in the system, achieving good convergence between these results and the analytical solutions.