Novel approximations to the non-linear fractional Belousov-Zhabotinsky reaction in the frame of Caputo operator

The Belousov-Zhabotinsky system is a highly studied system that offers continuing possibilities for understanding the fundamental principles of nonlinear dynamics in complex systems. We present novel approaches to the time-fractional Belousov-Zhabotinsky system as part of our efforts to gain a deeper understanding of this complex system. Utilizing both the homotopy perturbation transform method (HPTM) and the new iterative transform technique (NITM) aims to introduce new perspectives and methods to the ongoing discussion about this intriguing and significant field of study. We achieved a series of solutions to verify the precision of the recommended methodologies. The model’s behavior and the effects of varying the fractional order derivative in Caputo’s sense and time are illustrated through 2D and 3D graphical representations for a better understanding. Furthermore, basic tables are provided to compare the findings for integer and fractional orders. It is confirmed that the solution achieved using the methods provided converges at a suitable rate to the exact solution. Moreover, we compared our findings with those of the Double Laplace method (DLM), the Optimal Homotopy Asymptotic method (OHAM) and Shehu Adomian decomposition method (SADM). The comparison shows that our methods are more effective than alternative strategies. Additionally, we offer solution profiles that illustrate the behavior of the acquired findings, helping readers better understand the impact of the fractional order. These techniques also demonstrate the practical applications of fractal calculus. The findings of this study also provide validity to the importance and worth of fractional operators in practical applications.