An expansion based on Sine-Gordon equation to Solve KdV and modified KdV equations in conformable fractional forms

An expansion method based on time fractional Sine-Gordon equation is implemented to construct some real and complex valued exact solutions the Korteweg-de Vries modified equations in forms. Compatible traveling wave transform plays a key role be able apply homogeneous balance technique set predicted solution. The relation between trigonometric hyperbolic functions allows form with multiplication of powers functions. Some forms are explicitly expressed by proposed for both equations.