On stable manifolds for planar fractional differential equations

2014 ◽  
Vol 226 ◽  
pp. 157-168 ◽  
Author(s):  
N.D. Cong ◽  
T.S. Doan ◽  
S. Siegmund ◽  
H.T. Tuan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Stable Manifolds ◽  
Fractional Differential

scholarly journals On the center-stable manifolds for some fractional differential equations of Caputo type

2018 ◽  
Vol 23 (5) ◽  
pp. 642-663 ◽  
Author(s):  
Shan Peng ◽  
JinRong Wang ◽  
Xiulan Yu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence Results ◽  
Dimensional Case ◽  
High Dimensional ◽  
Stable Manifolds ◽  
Mild Conditions ◽  
Relaxation Factor ◽  
High Dimensional Case ◽  
Fractional Differential

This paper is devoted to study the existence of center-stable manifolds for some planar fractional differential equations of Caputo type with relaxation factor. After giving some necessary estimation for Mittag–Leffler functions, some existence results for center-stable manifolds are established under the mild conditions by virtue of a suitable Lyapunov–Perron operator. Moreover, an explicit example is given to illustrate the above result. Finally, high-dimensional case is considered.

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