Fractional derivative modeling of bioreaction-diffusion processes

摘要

The aim of this work is to analyze the application of fractional derivatives in time for the mathematical modeling of complex processes. As an example, a bioprocess is considered and the related distribution of nutrients, bacteria and bioproduct in multiphase fluid systems. The mathematical model under investigation includes convection, diffusion, bioreaction and boundary conditions at the interfaces: interface mass-transfer and adsorption. Different approaches of time-fractional modeling of a bioprocess are discussed. To evaluate the ability of a fractional order model to correctly reproduce the behavior that the underlying process must exhibit, numerical procedures are developed and computer simulations are performed.