Approximation of fractional-order Chemostat model with nonstandard finite difference scheme

Abstract

In this paper, the fractional-order form of three dimensional chemostat model with variable yields is introduced. The stability analysis of this fractional system is discussed in detail. In order to study the dynamic behaviours of mentioned fractional system, the well known nonstandardfinite difference (NSFD) scheme is implemented. The proposed NSFD scheme is compared with the forward Euler and fourth order Runge-Kutta methods. Numerical results show that the NSFD approach is easy and accurate when applied to fractional-order chemostat model.