Relative controllability analysis of fractional order differential equations with multiple time delays

被引：11

作者：

Vadivoo, B. S. ^{[1
]}

Jothilakshmi, G. ^{[1
]}

Almalki, Y. ^{[2
]}

Debbouche, A. ^{[3
]}

Lavanya, M. ^{[1
]}

机构：

[1] Alagappa Univ, Dept Math, Karaikkudi 630004, India

[2] King Khalid Univ, Coll Sci, Dept Math, Abha 61413, Saudi Arabia

[3] Guelma Univ, Dept Math, Guelma 24000, Algeria

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2022年 / 428卷

关键词：

Caputo fractional derivative; Delayed perturbation; Mittag-Leffler functions; Relative controllability; Grammian matrix; SYSTEMS;

D O I：

10.1016/j.amc.2022.127192

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the relative controllability for a class of fractional differential equations with multiple time delays. The solution representation is introduced for this system via multiple delayed perturbations of Mittag-Leffler function. Necessary and sufficient conditions for the indicated problem to be relatively controllable are established for linear and non-linear systems. For non-linear case, the existence result is proved by using Krasnoselskii's fixed point theorem. Numerical examples are given to illustrate the theoretical results, and its diagrammatic formulations are done by MATLAB.(c) 2022 Elsevier Inc. All rights reserved.

引用

页数：25

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