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

Pundikala Veeresha

doi:10.53391/mmnsa.2021.01.001

EN

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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Details

Primary Language

English

Subjects

Applied Mathematics

Journal Section

Research Article

Authors

Pundikala Veeresha ^* This is me
0000-0002-4468-3048
India

Publication Date

September 30, 2021

Submission Date

June 24, 2021

Acceptance Date

August 13, 2021

Published in Issue

Year 2021 Volume: 1 Number: 1

DOI

https://doi.org/10.53391/mmnsa.2021.01.001

IZ

https://izlik.org/JA79XN63LT

APA

Veeresha, P. (2021). A numerical approach to the coupled atmospheric ocean model using a fractional operator. Mathematical Modelling and Numerical Simulation With Applications, 1(1), 1-10. https://doi.org/10.53391/mmnsa.2021.01.001

AMA

1.Veeresha P. A numerical approach to the coupled atmospheric ocean model using a fractional operator. MMNSA. 2021;1(1):1-10. doi:10.53391/mmnsa.2021.01.001

Chicago

Veeresha, Pundikala. 2021. “A Numerical Approach to the Coupled Atmospheric Ocean Model Using a Fractional Operator”. Mathematical Modelling and Numerical Simulation With Applications 1 (1): 1-10. https://doi.org/10.53391/mmnsa.2021.01.001.

EndNote

Veeresha P (September 1, 2021) A numerical approach to the coupled atmospheric ocean model using a fractional operator. Mathematical Modelling and Numerical Simulation with Applications 1 1 1–10.

IEEE

[1]P. Veeresha, “A numerical approach to the coupled atmospheric ocean model using a fractional operator”, MMNSA, vol. 1, no. 1, pp. 1–10, Sept. 2021, doi: 10.53391/mmnsa.2021.01.001.

ISNAD

Veeresha, Pundikala. “A Numerical Approach to the Coupled Atmospheric Ocean Model Using a Fractional Operator”. Mathematical Modelling and Numerical Simulation with Applications 1/1 (September 1, 2021): 1-10. https://doi.org/10.53391/mmnsa.2021.01.001.

JAMA

1.Veeresha P. A numerical approach to the coupled atmospheric ocean model using a fractional operator. MMNSA. 2021;1:1–10.

MLA

Veeresha, Pundikala. “A Numerical Approach to the Coupled Atmospheric Ocean Model Using a Fractional Operator”. Mathematical Modelling and Numerical Simulation With Applications, vol. 1, no. 1, Sept. 2021, pp. 1-10, doi:10.53391/mmnsa.2021.01.001.

Vancouver

1.Pundikala Veeresha. A numerical approach to the coupled atmospheric ocean model using a fractional operator. MMNSA. 2021 Sep. 1;1(1):1-10. doi:10.53391/mmnsa.2021.01.001