Stability analysis for a class of nabla (q, h)-fractional difference equations

被引：15
|
作者：
Liu, Xiang [1 ]
Jia, Baoguo [1 ]
Erbe, Lynn [2 ]
Peterson, Allan [2 ]
机构：
[1] Sun Yat Sen Univ, Sch Math, Guangzhou, Guangdong, Peoples R China
[2] Univ Nebraska, Dept Math, Lincoln, NE USA
来源：
TURKISH JOURNAL OF MATHEMATICS | 2019年 / 43卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Nabla; (q; h)-fractional difference equations; stability; discrete fractional Lyapunov direct method; Lyapunov functions; MITTAG-LEFFLER STABILITY; LYAPUNOV FUNCTIONS;
D O I：
10.3906/mat-1811-96
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper investigates stability of the nabla (q, h)-fractional difference equations. Asymptotic stability of the special nabla (q, h)-fractional difference equations are discussed. Stability theorems for discrete fractional Lyapunov direct method are proved. Furthermore, we give some new lemmas (including important comparison theorems) related to the nabla (q, h)-fractional difference operators that allow proving the stability of the nabla (q, h)-fractional difference equations, by means of the discrete fractional Lyapunov direct method, using Lyapunov functions. Some examples are given to illustrate these results.
引用
收藏
页码：664 / 687
页数：24
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