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Trajectories and Singular Points of Two‐Dimensional Fractional‐Order Autonomous Systems

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  • Bohui Yang
  • Ziyang Luo
  • Xindong Zhang
  • Quan Tang
  • Juan Liu

Abstract

In this paper, we study the trajectories and singular points of two‐dimensional fractional‐order planar autonomous linear system involving the Caputo‐Fabrizio fractional derivative. By the corresponding fractional integral of the Caputo‐Fabrizio fractional derivative, we obtain the analytical solutions for the fractional‐order planar autonomous linear system, and then, we discuss the behavior of the trajectories for the mentioned autonomous linear system. Furthermore, we consider the existence of singular points in the trajectories. We discuss the conditions under which the singular point is stable or unstable. By determining the value range of the parameters, we obtain the theorems on the type of singular points. Finally, some examples are given to verify the analysis for the mentioned autonomous linear system.

Suggested Citation

  • Bohui Yang & Ziyang Luo & Xindong Zhang & Quan Tang & Juan Liu, 2022. "Trajectories and Singular Points of Two‐Dimensional Fractional‐Order Autonomous Systems," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:3722011
    DOI: 10.1155/2022/3722011
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    References listed on IDEAS

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    1. Fardi, Mojtaba & Khan, Yasir, 2021. "A novel finite difference-spectral method for fractal mobile/immobiletransport model based on Caputo–Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Owolabi, Kolade M., 2021. "Computational analysis of different Pseudoplatystoma species patterns the Caputo-Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
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