Version 1
: Received: 24 December 2017 / Approved: 25 December 2017 / Online: 25 December 2017 (10:31:11 CET)
How to cite:
Ersoy Hepson, O.; Korkmaz, A.; Hosseini, K.; Rezazadeh, H.; Eslami, M. An Expansion Based on Sine-Gordon Equation to Solve KdV and modified KdV Equations in Conformable Fractional Forms. Preprints2017, 2017120178. https://doi.org/10.20944/preprints201712.0178.v1.
Ersoy Hepson, O.; Korkmaz, A.; Hosseini, K.; Rezazadeh, H.; Eslami, M. An Expansion Based on Sine-Gordon Equation to Solve KdV and modified KdV Equations in Conformable Fractional Forms. Preprints 2017, 2017120178. https://doi.org/10.20944/preprints201712.0178.v1.
Cite as:
Ersoy Hepson, O.; Korkmaz, A.; Hosseini, K.; Rezazadeh, H.; Eslami, M. An Expansion Based on Sine-Gordon Equation to Solve KdV and modified KdV Equations in Conformable Fractional Forms. Preprints2017, 2017120178. https://doi.org/10.20944/preprints201712.0178.v1.
Ersoy Hepson, O.; Korkmaz, A.; Hosseini, K.; Rezazadeh, H.; Eslami, M. An Expansion Based on Sine-Gordon Equation to Solve KdV and modified KdV Equations in Conformable Fractional Forms. Preprints 2017, 2017120178. https://doi.org/10.20944/preprints201712.0178.v1.
Abstract
An expansion method based on time fractional Sine-Gordon equation is implemented to construct some real and complex valued exact solutions to the Korteweg-de Vries and modified Korteweg-de Vries equation in time fractional forms. Compatible fractional traveling wave transform plays a key role to be able to apply homogeneous balance technique to set the predicted solution. The relation between trigonometric and hyperbolic functions based on fractional Sine-Gordon equation allows to form the exact solutions with multiplication of powers of hyperbolic functions.
Keywords
sine-gordon expansion method; conformable time fractional KdV equation; conformable time fractional modified KdV equation; exact solution, traveling wave solution
Copyright:
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.
