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

Muhammad Nasir Ali,Turgut Ak,Sana Noor,Syed Muhammad Husnine

doi:10.18052/www.scipress.com/bmsa.20.1

Abstract

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.

Highlights

Many real world problems in science and engineering are modelled by using nonlinear partial differential equations (NPDEs)
Space-time fractional form of modified extended Zakharov-Kuznetsov equation (MEZK) is investigated for soliton solutions
Bright and dark soliton solutions are obtained with solitary wave ansatz method. (1⁄GG′) −expansion method is applied to get some other solutions

Summary

Introduction

Many real world problems in science and engineering are modelled by using nonlinear partial differential equations (NPDEs). Many real world problems are modelled via FDE’s in fluid dynamics Exact solutions of such models play an important role in the mathematical sciences [1,2,3,4,5,6,7,8,9]. Exact solutions of time-fractional Burgers equation, biological population model and space–time fractional Whitham–Broer–Kaup equations are calculated with (GG′⁄GG) −expansion method [10]. New extended trial equation method is used for finding the exact solution of a class of generalized fractional Zakhrov-Kuznetsov equation [16]. Improved fractional sub-equation method is utilized for calculating the exact solutions of (3+1)-dimensional generalized fractional KdV–Zakharov–Kuznetsov equations [17]. Generalized Kudryashov method is considered for timefractional differential equations [18]

Objectives

Conclusion