Indian Journal of Science and Technology
Year: 2019, Volume: 12, Issue: 3, Pages: 1-7
A. H. A. Ali1 , A. A. Soliman1* , M. A. Abdou2 and M. H. Emara1
1Department of Mathematics, College of Science, University of Bisha, Bisha, 61922, PO Box 344, Kingdom of Saudi Arabia; [email protected], [email protected]
2Department of Physics, College of Science, University of Bisha, Bisha 61922, PO Box 344, Kingdom of Saudi Arabia; [email protected]
*Author for correspondence
A. A. Soliman
Department of Mathematics, College of Science, University of Bisha, Bisha, 61922, PO Box 344, Kingdom of Saudi Arabia.
Email: [email protected]
Objectives: To find the new exact travelling wave solutions of fractional order space-time Zakharov– Kuznetsov (ZK) equation of ion-acoustic waves. Methods/Statistical: The fractional derivative is defined in the sense of modified Riemann- Liouville derivative to convert the fractional space-time ZK equation to nonlinear ordinary differential equation. The two proposed techniques the (ω'/ω)-expansion and extended (ω'/ω)-expansion methods are employed for constructing the new exact travelling wave solutions of ZK equation. Findings/Results: The obtained new exact travelling wave solutions of ZK equation include the hyperbolic function, rational function, and trigonometric function. Application: The results reveal that the two used methods here are effective and powerful methods and might be accustomed to establish the other solutions of nonlinear fractional partial differential equations that arising in nonlinear science.
Keywords: The (ω'/ω)-Expansion Method, The Extended (ω'/ω)-Expansion Method, The Modified Riemann- Liouville Derivative, Homogeneous Balance, The New Exact Travelling Wave Solutions
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