Optimal control and approximate controllability for fractional integrodifferential evolution equations with infinite delay of order r∈(1,2)

被引：52

作者：

Raja, Marimuthu Mohan ^{[1
]}

Vijayakumar, Velusamy ^{[1
]}

Shukla, Anurag ^{[2
]}

Nisar, Kottakkaran Sooppy ^{[3
]}

Sakthivel, Natarajan ^{[4
]}

Kaliraj, Kalimuthu ^{[5
]}

机构：

[1] Vellore Inst Technol, Sch Adv Sci, Dept Math, Vellore 632014, Tamil Nadu, India

[2] Rajkiya Engn Coll Kannauj, Dept Appl Sci, Kannauj, Uttar Pradesh, India

[3] Prince Sattam Bin Abdulaziz Univ, Coll Arts & Sci, Dept Math, Wadi Aldawaser, Saudi Arabia

[4] Bharathiar Univ, Dept Appl Math, Coimbatore, Tamil Nadu, India

[5] Univ Madras, Ramanujan Inst Adv Study Math, Chennai, Tamil Nadu, India

来源：

OPTIMAL CONTROL APPLICATIONS & METHODS | 2022年 / 43卷 / 04期

关键词：

approximate controllability; cosine families; fixed point theorem; fractional derivative; integrodifferential equations; Mainardi's Wright-type function; mild solutions; optimal controls; DIFFERENTIAL-EQUATIONS; NONLOCAL CONDITIONS; MILD SOLUTIONS; SOLVABILITY; INCLUSIONS; EXISTENCE; SYSTEMS; CAUCHY;

D O I：

10.1002/oca.2867

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This article investigates the issue of optimal control and approximate controllability results for fractional integrodifferential evolution equations with infinite delay of r is an element of(1,2) in Banach space. In the beginning, we analyze approximate controllability results for fractional integrodifferential evolution equations using the fractional calculations, cosine families, and Banach fixed point theorem. After, we developed the continuous dependence of the fractional integrodifferential evolution equations by using the Henry-Gronwall inequality. Furthermore, we tested the existence of optimal controls for the Lagrange problem. Lastly, an application is presented to illustrate the theory of the main results.

引用

页码：996 / 1019

页数：24

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