On a multi-fractional model for biogas production for a cellulose-based substrate

This article describes the production of biogas in a cellulose-based substrate using a multifractional dynamic model. The objective is to give more precise depiction of the nonlinear characteristics of the chemical reactions involved in anaerobic digestion. In addition well-posedness and consistency, we present the sensitivity analysis used to determine which system equations follow non-integer order dynamics. We illustrate the efficacy of the model with numerical simulations that compare experimental data with the conventional model. The multifractional model’s outputs are in good agreement with the biogas production process’s overall response, which may lead to more effective control strategies.