Ulam's-Type Stability of First-Order Impulsive Differential Equations with Variable Delay in Quasi-Banach Spaces

被引：50
|
作者：
Wang, JinRong [1 ]
Zada, Akbar [2 ]
Ali, Wajid [2 ]
机构：
[1] Guizhou Univ, Dept Math, Guiyang 550025, Guizhou, Peoples R China
[2] Univ Peshawar, Dept Math, Peshawar 25000, Pakistan
来源：
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION | 2018年 / 19卷 / 05期
关键词：
Hyers-Ulam-Rassias stability; Bellman-Gronwall-Bihari integral inequality; Quasi normed spaces; alpha-Holder's condition; FRACTIONAL INTEGRABLE IMPULSES; RASSIAS STABILITY; INEQUALITIES;
D O I：
10.1515/ijnsns-2017-0245
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper, Ulam's-type stabilities are studied for a class of first-order impulsive differential equations with bounded variable delays on compact interval with finite number of impulses. Results of stability are proved via newly established integral inequality of Bellman-Gronwall-Bihari type with delay for discontinuous functions. Using this inequality for the first time and assumption of alpha-Holder's condition instead of common Lipschitz condition is novelty of this paper. Moreover, solution is obtained in quasi-Banach spaces which is best suited for obtaining results under the assumptions of alpha-Holder's condition.
引用
收藏
页码：553 / 560
页数：8
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