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Feng’s First Integral Method Applied to the ZKBBM and the Generalized Fisher Space‐Time Fractional Equations

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Listed:
  • Huitzilin Yépez-Martínez
  • Ivan O. Sosa
  • Juan M. Reyes

Abstract

The fractional derivatives in the sense of the modified Riemann‐Liouville derivative and Feng’s first integral method are employed to obtain the exact solutions of the nonlinear space‐time fractional ZKBBM equation and the nonlinear space‐time fractional generalized Fisher equation. The power of this manageable method is presented by applying it to the above equations. Our approach provides first integrals in polynomial form with high accuracy. Exact analytical solutions are obtained through establishing first integrals. The present method is efficient and reliable, and it can be used as an alternative to establish new solutions of different types of fractional differential equations applied in mathematical physics.

Suggested Citation

  • Huitzilin Yépez-Martínez & Ivan O. Sosa & Juan M. Reyes, 2015. "Feng’s First Integral Method Applied to the ZKBBM and the Generalized Fisher Space‐Time Fractional Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnljam:v:2015:y:2015:i:1:n:191545
    DOI: 10.1155/2015/191545
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    References listed on IDEAS

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    1. Wazwaz, Abdul-Majid, 2008. "The extended tanh method for new compact and noncompact solutions for the KP–BBM and the ZK–BBM equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1505-1516.
    2. Feng, Zhaosheng, 2008. "Traveling wave behavior for a generalized fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 481-488.
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