Chemostat Model Analysis Using Various Kernels with Fractional Derivatives

The investigation involves utilizing a set of three ordinary differential equations to mathematically model the degradation process of a mixture containing phenol and p-cresol within a continuously agitated bioreactor. The primary focus lies in the stability analysis of equilibrium points within this model. Additionally, the research delves into exploring the influence of fractal dimension and fractional order on the model, incorporating fractal-fractional derivatives and employing three distinct types of kernels. To quantify the concentrations of phenol, p-cresol, and biomass, highly effective computational algorithms have been formulated, enhancing the precision and efficiency of data analysis. In conclusion, the proposed methodology’s soundness and accuracy are thoroughly scrutinized and affirmed through extensive computational simulations.