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

被引：71
|
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
收藏
页码：268 / 291
页数：24
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