The Fractionalization of Modified Logistic Equation to Predict the Growth of Microalgae Botryococcus sp.

Abstract

In this paper, a fractional – order modified logistic equation is proposed where the extended Monod model is considered for microalgae Botryococcus sp. growth. The fractional calculus approach was applied to the integer – order modified logistic equation. Hence, the well – known numerical approach, Adams-type predictor – corrector method was implemented to solve the fractional – order modified logistic equation. The numerical simulations were carried out to simulate the classical integer – order and the fractional – order equations in describing the real experimental data of microalgae Botryococcus sp. growth. The results show the fractional – order version of the equation is promising with the experimental data.