A Unified Analysis of Exact Traveling Wave Solutions for the Fractional-Order and Integer-Order Biswas–Milovic Equation: Via Bifurcation Theory of Dynamical System

• Zhang, Bei ^[1] ; Zhu, Wenjing ^[2] ; Xia Yonghui ^[3] ; Bai Yuzhen
  1. [1] Huaqiao University

     Huaqiao University

     China

     
  2. [2] China Jiliang University

     China Jiliang University

     China

     
  3. [3] Zhejiang Normal University

     Zhejiang Normal University

     China

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
• Idioma: inglés
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• Resumen

  • This paper presents a unified method to investigate exact traveling wave solutions of the nonlinear fractional-order and integer-order partial differential equations. We use the conformable fractional derivatives. The method is based on the bifurcation theory of planar dynamical systems. To show the effectiveness of this method, we choose Biswas–Milovic (for short, BM) equation with conformable derivative as an application. Also comparison is presented for the exact traveling wave solutions between the integer-order BM equation and fractional-order BM equation. It is believed that this approach can be extended to other nonlinear fractional-order partial differential equations.