New results on controllability of fractional evolution systems with order $ \alpha\in (1,2) $

Yong Zhou; Jia Wei He

doi:10.3934/eect.2020077

Article Contents

2021, Volume 10, Issue 3: 491-509. Doi: 10.3934/eect.2020077

This issue Previous Article Approximate controllability of nonlocal problem for non-autonomous stochastic evolution equations Next Article Conditional regularity for the 3D Navier-Stokes equations in terms of the middle eigenvalue of the strain tensor

New results on controllability of fractional evolution systems with order $ \alpha\in (1,2) $

Yong Zhou^1,2, , and
Jia Wei He^1,

1.
Faculty of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China
2.
Faculty of Information Technology, Macau University of Science and Technology, Macau 999078, China

^* Corresponding author: Yong Zhou
^* Corresponding author: Yong Zhou

Received: March 31, 2020

Revised: March 31, 2020

Early access: June 2020

Published: September 2021

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Abstract

This paper addresses some interesting results of mild solutions to fractional evolution systems with order $ \alpha\in (1,2) $ in Banach spaces as well as the controllability problem. Firstly, we deduce a new representation of solution operators and give a new concept of mild solutions for the objective equations by the Laplace transform and Mainardi's Wright-type function, and then we proceed to establish a new compact result of the solution operators when the sine family is compact. Secondly, the controllability results of mild solutions are obtained. Finally, an example is presented to illustrate the main results.

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Mathematics Subject Classification: 26A33, 34A08, 34K35, 35R11.

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