A novel method for the analytical solution of fractional Zakharov\u2013Kuznetsov equations

Rasool Shah,Poom Kumam,Muhammad Arif,Hassan Khan,Dumitru Baleanu

doi:10.1186/s13662-019-2441-5

Abstract

In this article, an efficient analytical technique, called Laplace–Adomian decomposition method, is used to obtain the solution of fractional Zakharov– Kuznetsov equations. The fractional derivatives are described in terms of Caputo sense. The solution of the suggested technique is represented in a series form of Adomian components, which is convergent to the exact solution of the given problems. Furthermore, the results of the present method have shown close relations with the exact approaches of the investigated problems. Illustrative examples are discussed, showing the validity of the current method. The attractive and straightforward procedure of the present method suggests that this method can easily be extended for the solutions of other nonlinear fractional-order partial differential equations.

Highlights

Over the past decade, fractional differential equations (FDEs) have gained a lot of attention of researchers due to their ability to enhance real-world issues, used in various fields of engineering and physics
Some emerging analytical approximate approaches for FDEs are homotopy analysis method (HAM) [4], variational iteration method (VIM) [5], generalized fractional Taylor series method [6,7,8,9], iterative fractional power series system to solve a number of fractional integrodifferential equations [10]; using the Kudryashov technique and trial solution technique, we obtained traveling wave approaches to a fractional, nonlinear Schrodinger problem [11,12,13]; analytical solution to solve a particular homogeneous time-invariant fractional
6 Conclusion We have investigated the analytical solution of fractional Zakharov–Kuznetsov equations using the Laplace–Adomian decomposition method

Summary

Introduction

Fractional differential equations (FDEs) have gained a lot of attention of researchers due to their ability to enhance real-world issues, used in various fields of engineering and physics. In the modern age it is impossible to imagine modeling of many real world problems without using fractional partial differential equations (FPDEs). Some emerging analytical approximate approaches for FDEs are homotopy analysis method (HAM) [4], variational iteration method (VIM) [5], generalized fractional Taylor series method [6,7,8,9], iterative fractional power series system to solve a number of fractional integrodifferential equations [10]; using the Kudryashov technique and trial solution technique, we obtained traveling wave approaches to a fractional, nonlinear Schrodinger problem [11,12,13]; analytical solution to solve a particular homogeneous time-invariant fractional

Discussion

Conclusion