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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

Special Issues: Recent Advances in Fractional Calculus with Real World Applications

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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© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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