A comparison between Caputo and Caputo-Fabrizio fractional derivatives for modelling Lotka-Volterra differential equations

08/10/2019

∙

by   Leila Eftekhari, et al.

∙

0

∙

share

In this paper, we apply the concept of the fractional calculus to study three-dimensional Lotka-Volterra differential equations. Our goal is to compare the results of this system with respect to Caputo and Caputo-Fabrizio fractional derivatives. According to the existence of non-singular kernel in the definition of Caputo-Fabrizio operator, we analyze the stability of the system and try to improve a numerical method based on a corrected Adams-Bashforth method. Numerical results show that the behaviors of the Lotka-Volterra system depend on the fractional derivative order as well as the differential operators.