Preprint Article Version 1 This version is not peer-reviewed

An Expansion Based on Sine-Gordon Equation to Solve KdV and modified KdV Equations in Conformable Fractional Forms

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. Preprints 2017, 2017120178 (doi: 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 (doi: 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.

Subject Areas

sine-gordon expansion method; conformable time fractional KdV equation; conformable time fractional modified KdV equation; exact solution, traveling wave solution

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