A numerical approach to the coupled atmospheric ocean model using a fractional operator

Abstract

In the present framework, the coupled mathematical model of the atmosphere-ocean system called El Nino-Southern Oscillation (ENSO) is analyzed with the aid Adams-Bashforth numerical scheme. The fundamental aim of the present work is to demonstrate the chaotic behaviour of the coupled fractional-order system. The existence and uniqueness are demonstrated within the frame of the fixed-point hypothesis with the Caputo--Fabrizio fractional operator. Moreover, we captured the chaotic behaviour for the attained results with diverse order. The effect of the perturbation parameter and others associated with the model is captured. The obtained results elucidate that, the present study helps to understand the importance of fractional order and also initial conditions for the nonlinear models to analyze and capture the corresponding consequence of the fractional-order dynamical systems.

Keywords

• Caputo–Fabrizio derivative
• El Nino-Southern oscillation model
• fixed point theorem

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