scholarly journals Controllability for a class of semilinear fractional evolution systems via resolvent operators

2019 ◽  
Vol 18 (1) ◽  
pp. 455-478 ◽  
Author(s):  
Daliang Zhao ◽  
◽  
Yansheng Liu ◽  
Xiaodi Li
Keyword(s):  
Resolvent Operators ◽  
Fractional Evolution Systems ◽  
Evolution Systems

scholarly journals On the finite approximate controllability for Hilfer fractional evolution systems with nonlocal conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 529-539
Author(s):  
Xianghu Liu
Keyword(s):  
Approximate Controllability ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Evolution System ◽  
Controlled Systems ◽  
Uniqueness Of The Solution ◽  
Fractional Evolution Systems ◽  
Evolution Systems

Abstract The aim of this study is to investigate the finite approximate controllability of certain Hilfer fractional evolution systems with nonlocal conditions. To achieve this, we first transform the mild solution of the Hilfer fractional evolution system into a fixed point problem for a condensing map. Then, by using the topological degree approach, we present sufficient conditions for the existence and uniqueness of the solution of the Hilfer fractional evolution systems. Using the variational approach, we obtain sufficient conditions for the finite approximate controllability of semilinear controlled systems. Finally, an example is provided to illustrate main results.

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

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Daliang Zhao ◽  
Yansheng Liu
Keyword(s):  
Time Delay ◽  
Banach Spaces ◽  
Resolvent Operator ◽  
Approximate Controllability ◽  
Nonlocal Conditions ◽  
Exact Controllability ◽  
Impulsive Effect ◽  
Research Prospect ◽  
Fractional Evolution Systems ◽  
Evolution Systems

<p style='text-indent:20px;'>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.</p>

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