Next Article in Journal
Investigation of the Stereochemical-Dependent DNA and RNA Binding of Arginine-Based Nucleopeptides
Previous Article in Journal
A New DEA Model for Evaluation of Supply Chains: A Case of Selection and Evaluation of Environmental Efficiency of Suppliers
Article Menu
Issue 4 (April) cover image

Export Article

Open AccessArticle

Analytical Solutions of Fractional Klein-Gordon and Gas Dynamics Equations, via the (G/G)-Expansion Method

1
Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan
2
Department of Mathematics, Allama Iqbal Open University, Islamabad 44000, Pakistan
3
Theoretical and Computational Science (TaCS) Center Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
4
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(4), 566; https://doi.org/10.3390/sym11040566
Received: 2 April 2019 / Revised: 12 April 2019 / Accepted: 14 April 2019 / Published: 19 April 2019
  |  
PDF [438 KB, uploaded 19 April 2019]
  |  

Abstract

In this article, the ( G / G ) -expansion method is used for the analytical solutions of fractional-order Klein-Gordon and Gas Dynamics equations. The fractional derivatives are defined in the term of Jumarie’s operator. The proposed method is based on certain variable transformation, which transforms the given problems into ordinary differential equations. The solution of resultant ordinary differential equation can be expressed by a polynomial in ( G / G ) , where G = G ( ξ ) satisfies a second order linear ordinary differential equation. In this paper, ( G / G ) -expansion method will represent, the travelling wave solutions of fractional-order Klein-Gordon and Gas Dynamics equations in the term of trigonometric, hyperbolic and rational functions. View Full-Text
Keywords: (G′/G)-expansion method; fractional Klein-Gordon equation; fractional Gas Dynamics equation; exact solutions (G′/G)-expansion method; fractional Klein-Gordon equation; fractional Gas Dynamics equation; exact solutions
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Khan, H.; Barak, S.; Kumam, P.; Arif, M. Analytical Solutions of Fractional Klein-Gordon and Gas Dynamics Equations, via the (G/G)-Expansion Method. Symmetry 2019, 11, 566.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top