Open AccessControllability of nonlinear fractional evolution systems in Banach spaces: A survey
Author(s) -
Zhao Deng-feng,
Yansheng Liu
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021083
Subject(s) - controllability , banach space , mathematics , nonlinear system , resolvent , prime (order theory) , pure mathematics , operator (biology) , combinatorics , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
This paper presents a survey for some recent research on the controllability of nonlinear fractional evolution systems (FESs) in Banach spaces. The prime focus is exact controllability and approximate controllability of several types of FESs, which include the basic systems with classical initial and nonlocal conditions, FESs with time delay or impulsive effect. In addition, controllability results via resolvent operator are reviewed in detail. At last, the conclusions of this work and the research prospect are presented, which provides a reference for further study.