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Formulation and Solution of Three Dimensional Space-Time Fractional KdV-Zakharov-Kuznetsov and Modified KdV-Zakharov-Kuznetsov Equation

Uttam Ghosh, Md Ramjan Ali, Susmita Sarkar, Shantanu Das


In the present paper, we have constructed two fractional non-linear evolution equations: Those are the space-time fractional KdV-Zakharov-Kuznetsov (KdV-ZK) equation and space-time modified fractional mKdV-Zakharov-Kuznetsov (mKdV-ZK) equation and obtained their exact analytical solutions using the modified fractional Sub-Equation method. Here the modified fractional derivative is used to establish the fractional order KdV-ZK and mKdV-ZK equation using the fractional variational principle. Finally, numerical simulation is done to represent the results graphically.


Space-time fractional KdV-Zakharov-Kuznetsov equation, Jumarie fractional derivative, Fractional variational principle, Modified fractional Sub-Equation method

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