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Local stable manifolds for nonlinear planar fractional differential equations with order 1< α <2
Author(s) -
Liao Binghui,
Zeng Caibin
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5817
Subject(s) - mathematics , nonlinear system , fractional calculus , lyapunov function , manifold (fluid mechanics) , order (exchange) , mathematical analysis , planar , differential equation , partial differential equation , function (biology) , center manifold , pure mathematics , physics , computer graphics (images) , finance , quantum mechanics , computer science , economics , mechanical engineering , hopf bifurcation , evolutionary biology , engineering , bifurcation , biology
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.