A novel conformable fractional approach to the Brusselator system with numerical simulation

Abstract

In this study, we delve into a comprehensive analysis of the Brusselator system, combining both analytical and numerical approaches. In summary, our initial approach involves revisiting the classic Brusselator system using a conformable fractional derivative-based approach. Starting from this innovative reformulation, we obtain a nonlinear Volterra-type equation. This transformation allows us to simultaneously demonstrate the existence and uniqueness of the solution, while providing us with the necessary tools to develop an efficient numerical approximation method to solve the problem. Subsequently, we present a numerical simulation based on the Nyström method.