Periodic wave analysis to the time-fractional phi-four and (2+1) dimensional CBS equations

Samsun Nahar Ananna,Tianqing An,Abdulla Al â€“ Mamun

doi:10.14419/ijpr.v9i2.31824

Samsun Nahar Ananna, Tianqing An + Show 1 more

Open Access

https://doi.org/10.14419/ijpr.v9i2.31824

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Abstract

In this paper, we investigate some innovative and exact travelling wave solutions to the time-fractional phi-four equation and the (2+1) dimensional Calogero-Bogoyavlanskil schilf (CBS) equation using the ( )-expansion method. Periodic solutions are displayed in hyperbolic, trigonometric, and rational function solutions. Subsequently, we construct some new solutions connecting the free parameters of the phi-four equation and the CBS equation, which are characterized into three complete forms: rational function, trigonometric function, and hyperbolic functions. Graphical representations of some attained solutions are also presented in this article. Hence, this study shows the efficiency and the easiness of the ( )-expansion technique with the assistance of emblematically computational software MATLAB and Mathematica.Â Â

Highlights

In engineering, fluid dynamics, plasma physics, applied mathematics, and mathematical physics, nonlinear fractional partial differential equations (FPDEs) model significant phenomena and applications
The goal of this study is to develop precise travelling waves analysis using the (G′/G2)-expansion technique to better understand the physical meaning of a diversity of the phi-four and Calogero-Bogoyavlanskil schilf (CBS) equations
We investigated the periodic wave analysis of phi-four and CBS equations using the (G′/G2)-expansion method

Summary

Introduction

Fluid dynamics, plasma physics, applied mathematics, and mathematical physics, nonlinear fractional partial differential equations (FPDEs) model significant phenomena and applications. To find traveling wave solutions, efforts have increased in the literature of practical mathematics. The goal of this study is to develop precise travelling waves analysis using the (G′/G2)-expansion technique to better understand the physical meaning of a diversity of the phi-four and CBS equations. In this part, the (G′/G2)-expansion technique is discoursed and assessed using the recommended methodology.

The nonlinear time-fractional Phi-four equation

The nonlinear time-fractional CBS equation

Graphical representation

Conclusion