ABSTRACT
This contribution aims to develop a numerical tool for solving inverse problems modeled by ordinary differential equations with fractional order. This consists of association between the Orthogonal Collocation Method in fractional context and the Stochastic Fractal Search algorithm. The results obtained with the extension of the Orthogonal Collocation Method in mathematical functions demonstrated the ability of this strategy in comparison with other numerical approaches. For the purposes of illustration, an inverse problem for the determination of model parameters and fractional order in laccase enzyme fermentation process considering real experimental data is proposed and solved. In relation to this study, it can be concluded that the increase in number of freedom degrees (fractional order is considered as a new design variable) increases the chance of a better fit between the model and experimental data.
Keywords:
inverse problems; fractional ordinary differential equation; stochastic fractal search; batch fermentation