EXISTENCE AND APPROXIMATE CONTROLLABILITY OF FRACTIONAL EVOLUTION EQUATIONS WITH NONLOCAL CONDITIONS VIA RESOLVENT OPERATORS

被引：77

作者：

Chen, Pengyu ^{[1
]}

Zhang, Xuping ^{[1
]}

Li, Yongxiang ^{[1
]}

机构：

[1] Northwest Normal Univ, Dept Math, Lanzhou 730070, Peoples R China

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2020年 / 23卷 / 01期

关键词：

approximate controllability; fractional evolution equations; nonlocal conditions; alpha-order solution operator; alpha-order resolvent operator; CAUCHY-PROBLEMS; DIFFERENTIAL-EQUATIONS; MILD SOLUTIONS; SYSTEMS; INCLUSIONS;

D O I：

10.1515/fca-2020-0011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we are concerned with the existence of mild solutions as well as approximate controllability for a class of fractional evolution equations with nonlocal conditions in Banach spaces. Sufficient conditions of existence of mild solutions and approximate controllability for the desired problem are presented by introducing a new Green's function and constructing a control function involving Gramian controllability operator. The discussions are based on Schauder's fixed point theorem as well as the theory of alpha-order solution operator and alpha-order resolvent operator. An example is given to illustrate the feasibility of our theoretical results.

引用

页码：268 / 291

页数：24

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