Approximate controllability of fractional neutral evolution systems of hyperbolic type

Xuan-Xuan Xi; Mimi Hou; Xian-Feng Zhou; Yanhua Wen

doi:10.3934/eect.2021035

Article Contents

2022, Volume 11, Issue 4: 1037-1069. Doi: 10.3934/eect.2021035

This issue Previous Article On a second-order functional evolution problem with time and state dependent maximal monotone operators Next Article Exact boundary null controllability for a coupled system of plate equations with variable coefficients

Approximate controllability of fractional neutral evolution systems of hyperbolic type

1.
School of Mathematical Sciences, Anhui University, Hefei 230039, China
2.
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China

^*Corresponding author: Xian-Feng Zhou
^*Corresponding author: Xian-Feng Zhou

Received: November 30, 2020

Revised: April 30, 2021

Early access: July 2021

Published: August 2022

This work is supported by the National Natural Science Foundation of China (11471015 and 11601003); Natural Science Foundation of Anhui Province (1508085MA01, 1608085MA12, 1708085MA15 and 2008085QA19); Program of Natural Science Research for Universities of Anhui Province (KJ2016A023) and Program of Anhui Jianzhu University (K1930096)

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Abstract

In this paper, we deal with fractional neutral evolution systems of hyperbolic type in Banach spaces. We establish the existence and uniqueness of the mild solution and prove the approximate controllability of the systems under different conditions. These results are mainly based on fixed point theorems as well as constructing a Cauchy sequence and a control function. In the end, we give an example to illustrate the validity of the main results.

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Mathematics Subject Classification: 26A33, 34A12, 34K37, 35A01, 93B05.

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