Approximate controllability and optimal controls of fractional dynamical systems of order 1 < q < 2 in Banach spaces

被引：0

作者：

Qin, Haiyong ^{[1
]}

Zuo, Xin ^{[1
]}

Liu, Jianwei ^{[1
]}

Liu, Lishan ^{[2
]}

机构：

[1] China Univ Petr, Dept Automat, Beijing 102249, Peoples R China

[2] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2015年

基金：

中国国家自然科学基金;

关键词：

fractional integrodifferential equations; fixed point theorems; approximate controllability; optimal controls; DIFFERENTIAL-EQUATIONS; NONLOCAL CONDITIONS; MILD SOLUTIONS; INTEGRODIFFERENTIAL EQUATIONS; EVOLUTION-EQUATIONS; SOBOLEV TYPE; EXISTENCE; UNIQUENESS; INCLUSIONS;

D O I：

10.1186/s13662-015-0399-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper investigates the approximate controllability and optimal controls of fractional dynamical systems of order 1 < q < 2 in Banach spaces. We research a class of fractional dynamical systems governed by fractional integrodifferential equations with nonlocal initial conditions. Using the Krasnosel'skii fixed point theorem and the Schauder fixed point theorem, the approximate controllability results are obtained under two cases of the nonlinear term. We also present the existence results of optimal pairs of the corresponding fractional control systems with a Bolza cost function. Finally, an application is given to illustrate the effectiveness of our main results.

引用

页码：1 / 17

页数：17

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Approximate controllability and optimal controls of fractional dynamical systems of order 1 &lt; q &lt; 2 in Banach spaces

Approximate controllability and optimal controls of fractional dynamical systems of order 1 < q < 2 in Banach spaces