N维非线性时滞分数阶微分方程初值问题的全局解

数学物理学报 ›› 2018, Vol. 38 ›› Issue (5): 903-910.

N维非线性时滞分数阶微分方程初值问题的全局解

王俊¹,王天璐²,温艳华¹,周先锋^1,*()

¹ 安徽大学数学科学学院合肥 230601
² 西北工业大学数学系西安 710072

收稿日期:2017-06-22 出版日期:2018-11-09 发布日期:2018-11-09
通讯作者: 周先锋 E-mail:zhouxf@ahu.edu.cn
基金资助:
国家自然科学基金(11471015);国家自然科学基金(11371027);国家自然科学基金(11601003);安徽省自然科学基金(1508085MA01);安徽省自然科学基金(1608085MA12);安徽省自然科学基金(1708085MA15);安徽省高等学校自然科学基金(KJ2016A023)

Global Solutions of IVP for N-Dimensional Nonlinear Fractional Differential Equations with Delay

Jun Wang¹,Tianlu Wang²,Yanhua Wen¹,Xianfeng Zhou^1,*()

¹ School of Mathematical Sciences, Anhui University, Hefei 230601
² Department of Mathematics, Northwestern Polytechnical University, Xi'an 710072

Received:2017-06-22 Online:2018-11-09 Published:2018-11-09
Contact: Xianfeng Zhou E-mail:zhouxf@ahu.edu.cn
Supported by:
the NSFC(11471015);the NSFC(11371027);the NSFC(11601003);the Natural Science Foundation of Anhui Province(1508085MA01);the Natural Science Foundation of Anhui Province(1608085MA12);the Natural Science Foundation of Anhui Province(1708085MA15);the Program of Natural Science Research for Universities of Anhui Province(KJ2016A023)

摘要/Abstract

摘要：

微分方程初值问题全局解的存在性是研究李雅普诺夫意义下稳定性的先决条件。该文旨在研究初值问题（1.10）-（1.11）全局解的存在性.首先得到了初值问题（1.10）-（1.11）局部解的存在性，推广了文献[14]的结果；然后基于得到的延拓定理，证明了初值问题（1.10）-（1.11）全局解的存在性和唯一性.

关键词: 非线性, 分数阶, 存在性, 时滞, 全局解

Abstract:

The existence of global solutions of initial value problems (IVP) for differential equations is a precondition to study their stability in Lyapunov sense. This paper aims to investigate the existence of the global solutions of the IVP (1.10)-(1.11). The existence of a local solution of the IVP (1.10)-(1.11) is obtained first, which is an extension of the paper[14]. Then based on our extension theorem, we prove that the existence and uniqueness of the global solution of the IVP (1.10)-(1.11).

Key words: Nonlinear, Fractional, Existence, Delay, Global solution

中图分类号:

O175.14

王俊,王天璐,温艳华,周先锋. N维非线性时滞分数阶微分方程初值问题的全局解[J]. 数学物理学报, 2018, 38(5): 903-910.

Jun Wang,Tianlu Wang,Yanhua Wen,Xianfeng Zhou. Global Solutions of IVP for N-Dimensional Nonlinear Fractional Differential Equations with Delay[J]. Acta mathematica scientia,Series A, 2018, 38(5): 903-910.

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