scholarly journals Erratum to: On stable manifolds for fractional differential equations in high-dimensional spaces

2016 ◽  
Vol 86 (3) ◽  
pp. 1895-1895 ◽  
Author(s):  
N. D. Cong ◽  
T. S. Doan ◽  
S. Siegmund ◽  
H. T. Tuan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
High Dimensional ◽  
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.

scholarly journals Triangular System of Higher Order Singular Fractional Differential Equations

2021 ◽  
Vol 45 (01) ◽  
pp. 81-101
Author(s):  
AMELE TAIEB ◽  
ZOUBIR DAHMANI
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence Result ◽  
High Dimensional ◽  
Dimensional System ◽  
Stability Of Solutions ◽  
Banach Contraction ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential ◽  
The Banach Contraction Principle

In this paper, we introduce a high dimensional system of singular fractional differential equations. Using Schauder fixed point theorem, we prove an existence result. We also investigate the uniqueness of solution using the Banach contraction principle. Moreover, we study the Ulam-Hyers stability and the generalized-Ulam-Hyers stability of solutions. Some illustrative examples are also presented.

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