On stable manifolds for planar fractional differential equations

In this paper, we establish a local stable manifold theorem near a hyperbolic equilibrium point for planar fractional differential equations. The construction of this stable manifold is based on the associated Lyapunov–Perron operator. An example is provided to illustrate the result.

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Bibliographic Details
Published in:Applied mathematics and computation 2014-01, Vol.226, p.157-168
Main Authors: Cong, N.D., Doan, T.S., Siegmund, S., Tuan, H.T.
Format: Article
Language:English
Subjects:
Caputo derivative
Computation
Construction
Differential equations
Fractional differential equations
Manifolds
Mathematical models
Operators
Stable manifold theorem
Theorems
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Description
Summary:In this paper, we establish a local stable manifold theorem near a hyperbolic equilibrium point for planar fractional differential equations. The construction of this stable manifold is based on the associated Lyapunov–Perron operator. An example is provided to illustrate the result.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2013.10.010