SUCCESSIVE APPROXIMATION: A SURVEY ON STABLE MANIFOLD OF FRACTIONAL DIFFERENTIAL SYSTEMS

被引：19
|
作者：
Sayevand, Khosro [1 ]
Pichaghchi, Kazem [1 ]
机构：
[1] Malayer Univ, Fac Math Sci, Malayer, Iran
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2015年 / 18卷 / 03期
关键词：
successive approximation; stable manifold theorem; Hartman-Grobman theorem; fractional differential systems; HOMOTOPY PERTURBATION METHOD; NUMERICAL SCHEME; EQUATIONS; STABILITY;
D O I：
10.1515/fca-2015-0038
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper outlines a reliable strategy to approximate the local stable manifold near a hyperbolic equilibrium point for nonlinear systems of differential equations of fractional order. Furthermore, the local behavior of these systems near a hyperbolic equilibrium point is investigated based on the fractional Hartman-Grobman theorem. The fractional derivative is described in the Caputo sense. The solution existence, uniqueness, stability and convergence of the proposed scheme is discussed. Finally, the validity and applicability of our approach is examined with the use of a solvable model method.
引用
收藏
页码：621 / 641
页数：21
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