Controllability of the time-varying fractional dynamical systems with a single delay in control

被引：4

作者：

Vishnukumar, K. S. ^{[1
]}

Sivalingam, S. M. ^{[1
]}

Ahmad, Hijaz ^{[2
,3
,4
,5
]}

Govindaraj, V. ^{[1
]}

机构：

[1] Natl Inst Technol Puducherry, Dept Math, Karaikal 609609, India

[2] Near East Univ, Operat Res Ctr Healthcare, TRNC Mersin 10, TR-99138 Nicosia, Turkiye

[3] Islamic Univ Madinah, Fac Sci, Dept Math, Madinah, Saudi Arabia

[4] Gulf Univ Sci & Technol, Ctr Appl Math & Bioinformat, Mishref, Kuwait

[5] Lebanese Amer Univ, Dept Comp Sci & Math, Beirut, Lebanon

来源：

NONLINEAR DYNAMICS | 2024年 / 112卷 / 10期

关键词：

Fractional dynamical systems; Delay systems; Controllability Grammian; Caputo fractional derivative; Fixed point theorem; LINEAR-SYSTEMS; WAVE-EQUATION; OBSERVABILITY;

D O I：

10.1007/s11071-024-09411-3

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

In this article, we explored the controllability of fractional dynamical systems with a single delay in the control function with the Caputo fractional derivative. It is the first work in which the author studies the controllability of a time-varying fractional dynamical system with a delay in the control function. We develop the necessary and sufficient criteria for the solution representation of controllability of time-varying fractional linear dynamical systems by utilizing the Grammian matrix. We use Schauder's fixed point theorem to establish sufficient conditions for the controllability of time-varying nonlinear fractional dynamical systems. With the help of successive approximation techniques, numerical examples validate the theoretical results.

引用

页码：8281 / 8297

页数：17

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