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Traveling wave solution of conformable fractional generalized reaction Duffing model by generalized projective Riccati equation method

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Abstract

The generalized projective Riccati equation method is proposed to establish exact solutions for generalized form of the reaction Duffing model in fractional sense namely, Khalil’s derivative. The compatible traveling wave transform converts the governing equation to a non linear ODE. The predicted solution is a series of two new variables that solve a particular ODE system. Coefficients of terms in the series are calculated by solving an algebraic system that comes into existence by substitution of the predicted solution into the ODE which is the result of the wave transformation of the governing equation. Returning original variables give exact solutions to the governing equation in various forms.

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Authors and Affiliations

  1. Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran

    Hadi Rezazadeh

  2. Department of Mathematics, Cankiri Karatekin University, Çankırı, Turkey

    Alper Korkmaz

  3. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

    Mostafa Eslami

  4. Department of Applied Mathematics, Iran University of Science and Technology, Tehran, Iran

    Javad Vahidi

  5. Faculties of Information, Communication and Technology, Malek-Ashtar University of Technology, Tehran, Iran

    Rahim Asghari

Authors
  1. Hadi Rezazadeh
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  2. Alper Korkmaz
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  3. Mostafa Eslami
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  4. Javad Vahidi
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  5. Rahim Asghari
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Correspondence to Mostafa Eslami.

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Rezazadeh, H., Korkmaz, A., Eslami, M. et al. Traveling wave solution of conformable fractional generalized reaction Duffing model by generalized projective Riccati equation method. Opt Quant Electron 50, 150 (2018). https://doi.org/10.1007/s11082-018-1416-1

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  • DOI: https://doi.org/10.1007/s11082-018-1416-1

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