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