Trajectories and Singular Points of Two-Dimensional Fractional-Order Autonomous Systems. (28th July 2022)

• Record Type: Journal Article
• Authors: Yang, Bohui; Luo, Ziyang; Zhang, Xindong; Tang, Quan; Liu, Juan
• Other Names: Alomari Mohammad Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2022(2022)
• Publication Date: 2022-07-28
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2022/3722011
• Languages: English
• ISSNs: 1687-9120

Abstract

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.