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Variational approach to fractal reaction-diffusion equations with fractal derivatives

Wu Yue (College of Economics and Management, Shanghai University of Political Science and Law, Qingpu area, Shanghai, China), needlewu@sina.com

A fractal modification of the reaction-diffusion process is proposed with fractal derivatives, and a fractal variational principle is established in a fractal space. The concentration of the substrate can be determined according to the minimal value of the variational formulation. The solution process is illustrated step by step for ease applications in engineering, and the effect of fractal dimensions on solution morphology is elucidated graphically.

Keywords: Fractal calculus, Reaction potential, Michalis-Menten kinetics, least action, ancient Chinese mathematics