Fractional order reaction-diffusion dynamics: A study via approximate analytical technique

Abstract

Lyons and colleagues proposed a model based on a second-order nonlinear differential equation to theoretically examine the steady-state of amperometric z behavior in polymer-modified electrode systems controlled by Michaelis-Menten (MM) kinetics. This study builds on previous work by extending the model to a Fractional Differential Equation (FDE) framework in order to better represent sequential dynamics. The impacts of different factors across multiple fractional orders 𝜇 are analyzed in order to derive approximated analytical solutions for the FDE system using the Homotopy Perturbation Method (HPM). The fractional-order technique allows for a smooth transition between fractional and integer-order dynamics and enables more flexibility for simulating complex reaction-diffusion phenomena. These findings contribute to a deeper understanding of the interaction between reaction kinetics and diffusion processes, opening new possibilities for advanced applications in electrochemical systems.