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Solutions of Fractional Konopelchenko‐Dubrovsky and Nizhnik‐Novikov‐Veselov Equations Using a Generalized Fractional Subequation Method

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  • Yanqin Liu
  • Limei Yan

Abstract

A new generalized fractional subequation method based on the relationship of fractional coupled equations is proposed. This method is applied to the space‐time fractional coupled Konopelchenko‐Dubrovsky equations and Nizhnik‐Novikov‐Veselov equations. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions, and rational solutions. It is observed that the proposed approach provides a simple and reliable tool for solving many other fractional coupled differential equations.

Suggested Citation

  • Yanqin Liu & Limei Yan, 2013. "Solutions of Fractional Konopelchenko‐Dubrovsky and Nizhnik‐Novikov‐Veselov Equations Using a Generalized Fractional Subequation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:839613
    DOI: 10.1155/2013/839613
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    References listed on IDEAS

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    1. Yanqin Liu, 2012. "Variational Homotopy Perturbation Method for Solving Fractional Initial Boundary Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-10, June.
    2. Yanqin Liu, 2012. "Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Yanqin Liu, 2012. "Variational Homotopy Perturbation Method for Solving Fractional Initial Boundary Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Jiang, Xiaoyun & Xu, Mingyu, 2010. "The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3368-3374.
    5. Yanqin Liu, 2012. "Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, April.
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