Analytical Study of the Complexities in a Three Species Food Web Model with Modified Caputo–Fabrizio Operator

Abstract

This article presents the analytical study of the three species fractional food web model in the framework of the Modified Caputo–Fabrizio operator. With the help of fixed point theory, the existence and uniqueness results are investigated for the fractional order model. To obtain the approximate solution for the suggested model, the well-known Laplace–Adomian decomposition method is used. The solutions are validated through simulations with a variety of fractional orders and initial values, where the complex nature of the system can be observed. The technique used here can be easily used to study a range of complex problems in different branches of science. From the figures, it can be observed that, at integer higher fractional order, there are a number of oscillations in the system and the system behaves chaotically, while, at lower fractional orders, the oscillation amplitudes decrease, resulting in the faster converging towards the equilibrium point. According to the results, the Modified Caputo–Fabrizio fractional-order derivative may be used in a variety of future fractional dynamics scenarios.