Approximate controllability of impulsive fractional evolution equations of order 1 < α < 2 with state-dependent delay in Banach spaces

被引：2

作者：

Arora, Sumit ^{[1
]}

Mohan, Manil T. ^{[2
]}

Dabas, Jaydev ^{[1
]}

机构：

[1] Indian Inst Technol Roorkee IIT Roorkee, Dept Appl Sci & Engn, Roorkee 247667, Uttar Pradesh, India

[2] Indian Inst Technol Roorkee IIT Roorkee, Dept Math, Roorkee, Uttar Pradesh, India

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 01期

关键词：

approximate controllability; fractional derivative; Mainardi's Wright-type function; noninstantaneous impulses; state-dependent delay; DIFFERENTIAL-EQUATIONS; MILD SOLUTIONS; NONLOCAL CONDITIONS; SYSTEMS; MODEL; INCLUSIONS; EXISTENCE;

D O I：

10.1002/mma.8527

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article deals with the approximate controllability problem for fractional evolution equations involving noninstantaneous impulses and state-dependent delay. In order to derive sufficient conditions for the approximate controllability of our problem, we first consider the linear-regulator problem and find the optimal control in the feedback form. By using this optimal control, we develop the approximate controllability of the linear fractional control system. Further, we obtain sufficient conditions for the approximate controllability of the nonlinear problem. In the end, we provide a concrete example to support the applicability of the derived results.

引用

页码：531 / 559

页数：29

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