Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators-Reference-Cited by-同舟云学术

Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators

Published:2020-02-01 Issue:1 Volume:23 Page:268-291
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Chen Pengyu¹,Zhang Xuping¹,Li Yongxiang¹

Affiliation:

1. Department of Mathematics , Northwest Normal University , Lanzhou , 730070 , People’s Republic of China

Abstract

Abstract 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 α-order solution operator and α-order resolvent operator. An example is given to illustrate the feasibility of our theoretical results.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2020-0011/pdf

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