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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics Science, Huaqiao University, Quanzhou, 362000, China

    Bei Zhang

  2. Department of Mathematics, China Jiliang University, Hangzhou, 310018, China

    Wenjing Zhu

  3. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Yonghui Xia

  4. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China

    Yuzhen Bai

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  1. Bei Zhang
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This work was jointly supported by the National Natural Science Foundation of China under Grant (Nos. 11671176, 11931016, 11901547, 11871251), Natural Science Foundation of Zhejiang Province under Grant (No. LY20A010016), and start-up fund of Huaqiao University.

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Zhang, B., Zhu, W., Xia, Y. et al. A Unified Analysis of Exact Traveling Wave Solutions for the Fractional-Order and Integer-Order Biswas–Milovic Equation: Via Bifurcation Theory of Dynamical System. Qual. Theory Dyn. Syst. 19, 11 (2020). https://doi.org/10.1007/s12346-020-00352-x

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