Strong Interacting Internal Waves in Rotating Ocean: Novel Fractional Approach

Pundikala Veeresha,Wei Gao,Haci Mehmet Baskonus

doi:10.3390/axioms10020123

Pundikala Veeresha, Wei Gao + Show 1 more

Open Access

https://doi.org/10.3390/axioms10020123

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Abstract

The main objective of the present study is to analyze the nature and capture the corresponding consequences of the solution obtained for the Gardner–Ostrovsky equation with the help of the q-homotopy analysis transform technique (q-HATT). In the rotating ocean, the considered equations exemplify strong interacting internal waves. The fractional operator employed in the present study is used in order to illustrate its importance in generalizing the models associated with kernel singular. The fixed-point theorem and the Banach space are considered to present the existence and uniqueness within the frame of the Caputo–Fabrizio (CF) fractional operator. Furthermore, for different fractional orders, the nature has been captured in plots. The realized consequences confirm that the considered procedure is reliable and highly methodical for investigating the consequences related to the nonlinear models of both integer and fractional order.

Highlights

There is always a door open for innovation, novelty, improvisation, and modifications in the research when it comes to the investigation of consequences that help us to solve real-world problems and in this connection, many researchers have derived stimulating results with the aid of fractional calculus (FC), and by using efficient techniques with the aid of fundamental results of FC [7,8,9,10]
We capture the physical nature of two cases with different fractional order, small-scale dispersion, and homotopy parameters
It is essential to illustrate the effect of the fractional operator incorporated in the considered model

Summary

Introduction

Even though pioneers propose many new notions, many things need to be derived in order to ensure all classes of phenomena, which will be achieved by overcoming the limitations raised by mathematicians and scientists [1,2,3,4,5,6,7]. This is true when researchers try to study, analyze and predict behaviors related to history, long-range memory, heritage, chaos, epidemiology, and other such subjects. There is always a door open for innovation, novelty, improvisation, and modifications in the research when it comes to the investigation of consequences that help us to solve real-world problems (the present pandemic, for example) and in this connection, many researchers have derived stimulating results with the aid of FC, and by using efficient techniques with the aid of fundamental results of FC [7,8,9,10]

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