A fractional calculus approach to the dynamic optimization of biological reactive systems. Part I: Fractional models for biological reactions

This series of two papers is concerned with both the modeling and the optimization of systems whose governing equations contain fractional derivative operators. In this first work, we show that the dynamics of some reactive systems displaying atypical behavior can be represented by fractional order differential equations. We consider three different instances of fermentation processes and one case of a thermal hydrolysis process. We propose a fractional fermentation model and, based on experimental data, a non-linear fitting approach that includes fractional integration is used to obtain the fractional orders and kinetics parameters. On the other hand, since the ordinary thermal hydrolysis model used as a reference was derived from fundamental principles, a formal fractionalization approach was used in this work to obtain the corresponding fractional model. Results show the feasibility and capabilities of fractional calculus as a tool for modeling dynamic systems in the area of process systems engineering.