Fractional Order for Food Gums: Modeling and Simulation

Fractional order calculus can represent systems with high-order dynamics and complex nonlinear phenomena using few coefficients, since the arbitrary order of the derivatives provides an additional degree of freedom to fit a specific behavior. Numerous mathematicians have contributed to the history of fractional calculus by attempting to solve a fundamental problem to the best of their understanding. Each researcher sought a definition and therefore different approaches, which has led to various definitions of differentiation and anti-differentiation of non-integer orders that are proven equivalent. Although all these definitions may be equivalent, from one specific standpoint, i.e., for a specific application, some definitions seem more attractive. Furthermore, it is well known that food gums are complex carbohydrates that can suit for a wide variety of functions in the context of food engineering. The viscoelastic behavior of food gums is crucial for these applications and formulations of new or improved food products. Small progress has been made to understand the viscoelastic behavior of food gums and there are few studies in the literature about these models. In this paper, we applied the Riemann-Liouville approach and the Fourier transform in order to obtain numerical simulations results of a fractional derivative model based on previous literature that to make a quantitative description of the viscoelastic properties behavior for a food gum. The results reveal that the fractional model shows good simulation capability and can be an attractive means for predicting and to elucidate the dynamic viscoelastic behavior of food gums.