Travelling wave solutions for fractional Korteweg-de Vries equations via an approximate-analytical method

Hayman Thabet; Subhash Kendre; James Peters; Hayman Thabet; Subhash Kendre; James Peters

doi:10.3934/math.2019.4.1203

AIMS Mathematics

2019, Volume 4, Issue 4: 1203-1222. doi: 10.3934/math.2019.4.1203

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Travelling wave solutions for fractional Korteweg-de Vries equations via an approximate-analytical method

1.
Department of Mathematics, Savitribai Phule Pune University, Pune 411007, India
2.
Computational Intelligence Laboratory, University of Manitoba, WPG, MB, R3T 5V6, Winnipeg, Canada
3.
Department of Mathematics, Faculty of Arts and Science, Adiyaman University, 02040 Adiyaman, Turkey

Received: 29 December 2019 Accepted: 26 February 2019 Published: 26 August 2019

This paper introduces an approximate-analytical method (AAM) for solving nonlinear fractional partial differential equations (NFPDEs) in full general forms. The main advantage of the paper is to apply the proposed AAM to solve the fractional Korteweg-de Vries (KdV) equations. Moreover, the analytical travelling wave solutions for the fractional KdV equation and the modified fractional KdV equation are successfully obtained. The numerical solutions are also obtained in the forms of tables and graphs. The fractional partial derivatives are considered in Caputo sense.
- approximate-analytical method,
- nonlinear fractional partial differential equations,
- fractional KdV equations,
- traveling wave solutions
Citation: Hayman Thabet, Subhash Kendre, James Peters. Travelling wave solutions for fractional Korteweg-de Vries equations via an approximate-analytical method[J]. AIMS Mathematics, 2019, 4(4): 1203-1222. doi: 10.3934/math.2019.4.1203

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Abstract

This paper introduces an approximate-analytical method (AAM) for solving nonlinear fractional partial differential equations (NFPDEs) in full general forms. The main advantage of the paper is to apply the proposed AAM to solve the fractional Korteweg-de Vries (KdV) equations. Moreover, the analytical travelling wave solutions for the fractional KdV equation and the modified fractional KdV equation are successfully obtained. The numerical solutions are also obtained in the forms of tables and graphs. The fractional partial derivatives are considered in Caputo sense.

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