Submitted:
24 December 2017
Posted:
25 December 2017
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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
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