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White Noise Functional Solutions for Wick‐Type Stochastic Fractional Mixed KdV‐mKdV Equation Using Extended (G′/G)‐Expansion Method

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  • Zhao Li
  • Peng Li
  • Tianyong Han

Abstract

In this paper, white noise functional solutions of Wick‐type stochastic fractional mixed KdV‐mKdV equations have been obtained by using the extended (G′/G)‐expansion method and the Hermite transform. Firstly, the Hermite transform is used to transform Wick‐type stochastic fractional mixed KdV‐mKdV equations into deterministic fractional mixed KdV‐mKdV equations. Secondly, the exact traveling wave solutions of deterministic fractional mixed KdV‐mKdV equations are constructed by applying the extended (G′/G)‐expansion method. Finally, a series of white noise functional solutions are obtained by the inverse Hermite transform.

Suggested Citation

  • Zhao Li & Peng Li & Tianyong Han, 2021. "White Noise Functional Solutions for Wick‐Type Stochastic Fractional Mixed KdV‐mKdV Equation Using Extended (G′/G)‐Expansion Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:9729905
    DOI: 10.1155/2021/9729905
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    References listed on IDEAS

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    1. Odibat, Zaid M., 2009. "Exact solitary solutions for variants of the KdV equations with fractional time derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1264-1270.
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