Local stable manifolds for nonlinear planar fractional differential equations with order 1<α<2

This paper reports the local stable manifolds near hyperbolic equilibria for nonlinear planar fractional differential equations of order 1<α<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.