New exact wave solutions to the space-time fractional-coupled Burgers equations and the space-time fractional foam drainage equation

M Nurul Islam,M Ali Akbar,Bernardo Spagnolo

doi:10.1080/23311940.2017.1422957

M Nurul Islam, M Ali Akbar + Show 1 more

Open Access

https://doi.org/10.1080/23311940.2017.1422957

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Journal: Cogent Physics	Publication Date: Jan 1, 2018
Citations: 25	License type: CC BY 4.0

Affiliation: Islamic University, University of Rajshahi

Abstract

The space-time fractional-coupled Burgers equations and the space-time fractional foam drainage equation are important as an electro-hydro-dynamical model to progress the local electric field and i...

Highlights

In recent years, non-linear fractional differential equations (NFDEs) have been attracted much interest and it has gained popularity among the researchers
It is remarkable to see that the traveling wave solution w1, w2, w3, w4, w5, w6, w7, w8, and w9 of the space-time fractional-coupled Burgers equations and space-time fractional foam drainage equation are fresh and further more general and have not been established in the previous solutions
We have obtained more new wave solutions by used the generalized (G′/G)-expansion method for these equations which have not been reported in the previous literature

Summary

Introduction

Non-linear fractional differential equations (NFDEs) have been attracted much interest and it has gained popularity among the researchers. D and k into Equation (3.4), we attain more general type and new exact traveling wave solutions of the non-linear fractional differential Equation (3.1). The coupled burgers equations In this sub-section, we determine some new close form traveling wave solutions to the space-time fractional-coupled Burgers equations by making use of the generalized (G′/G)-expansion method. The foam drainage equation we determine some appropriate close form traveling wave solutions to the spacetime fractional foam drainage equation by making use of the generalized (G′/G)-expansion method. The fractional foam drainage equation is a model of the flow of liquid through the channels and nodes between the bubbles, driven by gravity and capillarity This equation is described as the demandable model of waves on shallow water surface, ion acoustic waves in plasma, and the waves on foam maybe explain in terms of a non-linear PDE for the foam density as a function of time and vertical position.

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Results and discussion

Conclusion