The two variable (φ/φ, 1/φ)-expansion method for solving the time-fractional partial differential equations

Yunmei Zhao; Yinghui He; Huizhang Yang; Yunmei Zhao; Yinghui He; Huizhang Yang

doi:10.3934/math.2020264

AIMS Mathematics

2020, Volume 5, Issue 5: 4121-4135. doi: 10.3934/math.2020264

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Research article

The two variable (φ/φ, 1/φ)-expansion method for solving the time-fractional partial differential equations

College of Mathematics, Honghe University, Mengzi, Yunnan, 661199, China

Received: 16 January 2020 Accepted: 13 April 2020 Published: 28 April 2020
MSC : 35C25, 35C07, 35C08, 35Q20

In this paper, we apply the two variable (ϕ'/ϕ, 1/ϕ)-expansion method to seek exact traveling wave solutions (solitary wave solutions, periodic function solutions, rational function solution) for time-fractional Kuramoto-Sivashinsky (K-S) equation, (3+1)-dimensional time-fractional KdV-Zakharov-Kuznetsov (KdV-ZK) equation and time-fractional Sharma-Tasso-Olver (FSTO) equation. The solutions are obtained in the form of hyperbolic, trigonometric and rational functions containing parameters. The results show that the two variable (ϕ'/ϕ, 1/ϕ)-expansion method is simple, effctivet, straightforward and is the generalization of the (G'/G)-expansion method.
- the two variable (φ'/φ, 1/φ)-expansion method,
- nonlinear fractional differential equation,
- traveling wave solution
Citation: Yunmei Zhao, Yinghui He, Huizhang Yang. The two variable (φ/φ, 1/φ)-expansion method for solving the time-fractional partial differential equations[J]. AIMS Mathematics, 2020, 5(5): 4121-4135. doi: 10.3934/math.2020264

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Abstract

In this paper, we apply the two variable (ϕ'/ϕ, 1/ϕ)-expansion method to seek exact traveling wave solutions (solitary wave solutions, periodic function solutions, rational function solution) for time-fractional Kuramoto-Sivashinsky (K-S) equation, (3+1)-dimensional time-fractional KdV-Zakharov-Kuznetsov (KdV-ZK) equation and time-fractional Sharma-Tasso-Olver (FSTO) equation. The solutions are obtained in the form of hyperbolic, trigonometric and rational functions containing parameters. The results show that the two variable (ϕ'/ϕ, 1/ϕ)-expansion method is simple, effctivet, straightforward and is the generalization of the (G'/G)-expansion method.

References

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