Local stable manifolds for nonlinear planar fractional differential equations with order 1

作者：Liao, Binghui; Zeng, Caibin^*

来源：MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44(10): 8150-8165.

DOI：10.1002/mma.5817

• fractional calculus
• fractional dynamical system
• Lyapunov-Perron operator
• Mittag-Leffler function
• stable manifold

This paper reports the local stable manifolds near hyperbolic equilibria for nonlinear planar fractional differential equations of order 1<alpha<2. By using several useful estimates of Mittag-Leffler function and fractional calculus technique, we construct two suitable Lyapunov-Perron operators and set up their fixed points as the desired stable manifolds. We further present a specific example to compute explicitly the corresponding stable manifold as the application.