### Electronic Research Archive

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

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

• 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.

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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• 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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