A numerical method for discrete fractional--order chemostat model derived from nonstandard numerical 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 the mentioned fractional system‎, ‎the well known nonstandard (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.