Exact solutions and Hyers-Ulam stability of fractional equations with double delays

被引：6

作者：

Liang, Yixing ^{[1
]}

Shi, Yang ^{[1
]}

Fan, Zhenbin ^{[1
]}

机构：

[1] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Jiangsu, Peoples R China

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2023年 / 26卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Delay differential equations; Mittag-Leffler type functions; Fractional ordinary differential equations; Hyers-Ulam stability; FINITE-TIME STABILITY; DIFFERENTIAL-EQUATIONS; RELATIVE-CONTROLLABILITY; REPRESENTATION; SYSTEMS;

D O I：

10.1007/s13540-022-00122-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we discuss the exact solutions of linear homogeneous and nonhomogeneous fractional differential equations with double delays. Firstly, a new concept of double-delayed Mittag-Leffler type matrix function is introduced, which is the promotion of the double-delayed matrix exponential. Secondly, we apply the double-delayed Mittag-Leffler type matrix function and Laplace transform approach to obtain the exact solutions of fractional differential equations with double delays. Furthermore, the solution is used to investigate the Hyers-Ulam stability of the system. Lastly, we illustrate our techniques by an example.

引用

页码：439 / 460

页数：22

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