A research paper has been published by:

Asst. Prof. Dr. Ahmed Intisar Ghathith

Lecturer Dr. Al-Mu’tasim Abdul-Muhsin Hamid

Prof. Dr. Ahmed Farouk Qasim

Titled:

“Improving Solutions for the Nonlinear Fractional Belousov–Zhabotinsky System Using Particle Swarm Optimization Algorithms Based on He’s Polynomials”

Journal: *Mathematical Methods in the Applied Sciences*

Publication Date: September 27, 2026

DOI Link: https://doi.org/10.1002/mma.70949

Indexed in Scopus (Q1) and Clarivate (Q1)

Abstract:

Polynomials are employed to solve a wide range of nonlinear and fractional equations and systems representing diverse natural phenomena, including chemical systems that exhibit periodic and nonlinear behavior—such as the nonlinear fractional Belousov–Zhabotinsky system. These polynomials generate a series of mathematical terms that help characterize the system’s behavior and highlight its nonlinear properties. In this study, He’s polynomials were utilized to derive a series representing the system’s periodic and nonlinear behavior under various initial conditions.

To enhance the accuracy of the analysis regarding the chemical system’s behavior, the Particle Swarm Optimization (PSO) algorithm was employed to determine the impact of system parameters during the solution process. The algorithm demonstrated exceptional precision in parameter selection, thereby facilitating the analysis of periodic stability and the distinct transitions in the system’s behavior. The obtained results also demonstrated good agreement and close correspondence with analytical solutions, thereby supporting the efficiency of the employed method in representing the dynamic behavior of the chemical system under study.