Abstract
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
Highlights
During this paper the target of our aim by means that two proposed methods, namely and extended – expansions methods to solve the following fractional space-time in nonlinear of ion-acoustic waves arising in plasma physics as[29,30,31]
Step 4: Inserting Eq(3.4a) into Eq (3.3a) with Eq (3.5a), equating the order of the same order of to be zero, we get the set of algebraic equations for βi, c, λ and μ
The-expansion and the extended-expansion methods have been applied for obtaining the new exactsolutions of Zakharov– Kuznetsov (ZK) equation of fractional order arising in physics
Summary
The fractional calculus has a wide array namely, nonlinear optic, solid state physics, fluid flow, plasma physics, control theory, signal processing, systems identifications, biology[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] and so on. During this paper the target of our aim by means that two proposed methods, namely and extended – expansions methods to solve the following fractional space-time in nonlinear of ion-acoustic waves arising in plasma physics as[29,30,31]. This paper has been outlined as follows: Section 2represents the modified Riemann- Liouville derivative and it’s a few properties.
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