Controllability of nonlinear fractional evolution systems in Banach spaces: A survey

Daliang Zhao; Yansheng Liu; Daliang Zhao; Yansheng Liu

doi:10.3934/era.2021083

Electronic Research Archive

2021, Volume 29, Issue 5: 3551-3580. doi: 10.3934/era.2021083

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Controllability of nonlinear fractional evolution systems in Banach spaces: A survey

Daliang Zhao ,
Yansheng Liu ^,

School of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong 250014, China

Received: 01 June 2021 Revised: 01 August 2021 Published: 11 October 2021
Primary: 93B05, 47D06, 34K30; Secondary: 35R11

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.
- Controllability,
- fractional evolution systems,
- mild solutions,
- impulse,
- time delay,
- fixed point theorem
Citation: Daliang Zhao, Yansheng Liu. Controllability of nonlinear fractional evolution systems in Banach spaces: A survey[J]. Electronic Research Archive, 2021, 29(5): 3551-3580. doi: 10.3934/era.2021083

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Abstract

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.

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