On the fractional order space-time nonlinear equations arising in plasma physics

2018 ◽  
Vol 93 (4) ◽  
pp. 537-541 ◽  
Author(s):  
M A Abdou
Keyword(s):  
Plasma Physics ◽  
Nonlinear Equations ◽  
Fractional Order ◽  
Space Time

scholarly journals Soliton Solutions of Space-Time Fractional-Order Modified Extended Zakharov-Kuznetsov Equation in Plasma Physics

2018 ◽  
Vol 20 ◽  
pp. 1-8
Author(s):  
Muhammad Nasir Ali ◽  
Syed Muhammad Husnine ◽  
Sana Noor ◽  
Turgut Ak
Keyword(s):  
Differential Equation ◽  
Plasma Physics ◽  
Fractional Order ◽  
Physical Phenomenon ◽  
Nonlinear Partial Differential Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Space Time ◽  
Magnetized Plasma ◽  
Ansatz Method

The aim of this article is to calculate the soliton solutions of space-time fractional-order modified extended Zakharov-Kuznetsov equation which is modeled to investigate the waves in magnetized plasma physics. Fractional derivatives in the form of modified Riemann-Liouville derivatives are used. Complex fractional transformation is applied to convert the original nonlinear partial differential equation into another nonlinear ordinary differential equation. Then, soliton solutions are obtained by using (1/G')-expansion method. Bright and dark soliton solutions are also obtain with ansatz method. These solutions may be of significant importance in plasma physics where this equation is modeled for some special physical phenomenon.

scholarly journals Abundant wave solutions of conformable space-time fractional order Fokas wave model arising in physical sciences

2021 ◽  
Vol 60 (2) ◽  
pp. 2687-2696
Author(s):  
Shahzad Sarwar ◽  
Khaled M. Furati ◽  
Muhammad Arshad
Keyword(s):  
Fractional Order ◽  
Wave Model ◽  
Space Time ◽  
Physical Sciences ◽  
Wave Solutions

A novel approach for nonlinear equations occurs in ion acoustic waves in plasma with Mittag-Leffler law

2020 ◽  
Vol 37 (6) ◽  
pp. 1865-1897 ◽  
Author(s):  
P. Veeresha ◽  
D.G. Prakasha ◽  
Jagdev Singh
Keyword(s):  
Nonlinear Equations ◽  
Fractional Order ◽  
Nonlinear Differential Equations ◽  
Content Type ◽  
Physical Behaviour ◽  
Special Cases ◽  
Analysis Scheme ◽  
Laplace Transform Technique ◽  
The Future ◽  
Homotopy Analysis

Purpose The purpose of this paper is to find the solution for special cases of regular-long wave equations with fractional order using q-homotopy analysis transform method (q-HATM). Design/methodology/approach The proposed technique (q-HATM) is the graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme and fractional derivative defined with Atangana-Baleanu (AB) operator. Findings The fixed point hypothesis considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional-order model. To illustrate and validate the efficiency of the future technique, the authors analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order. Originality/value To illustrate and validate the efficiency of the future technique, we analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order. The obtained results elucidate that, the proposed algorithm is easy to implement, highly methodical, as well as accurate and very effective to analyse the behaviour of nonlinear differential equations of fractional order arisen in the connected areas of science and engineering.

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