An expansion based on Sine-Gordon equation to Solve KdV and modified KdV equations in conformable fractional forms
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 equations 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. Some exact solutions in traveling wave forms are explicitly expressed by the proposed method for both the Korteweg-de Vries and modified Korteweg-de Vries equations.
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References
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