A comparative analysis of Noyes-Field model for the non-linear Belousov–Zhabotinsky reaction using two reliable techniques

Abstract

Within the domain of nonlinear dynamics, the Belousov-Zhabotinsky reaction system has consistently captivated researchers, sustaining its position as a vibrant and dynamic area of exploration. As an enduring subject of study, the Belousov-Zhabotinsky system provides continuous opportunities to unravel the foundational tenets of nonlinear dynamics within intricate systems. In our quest to deepen comprehension of this complex system, we introduce an innovative methodology for addressing the time fractional Belousov-Zhabotinsky system. This novel approach leverages both the Natural Transform Iterative Method (NTIM) and the Optimal Homotopy Asymptotic Method (OHAM), aiming to contribute novel insights and methodologies to the ongoing discourse surrounding this intriguing and influential area of research. We obtained a series solution to test the accuracy of the suggested approach. The proposed technique has the advantage of requiring few calculations while producing high-precision results. To help you better understand, 2D and 3D graphical representations are provided to demonstrate the model's behavior and how changing the fractional order derivative in Caputo's sense and time affects the solutions.

Keywords

• Belousov–Zhabotinsky system
• Natural transform iterative method
• Caputo operator
• Optimal homotopy asymptotic method