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Research Article | Open Access

On the controllability results of semilinear delayed evolution systems involving fractional derivatives in Banach spaces

College of Science, Gansu Agricultural University, Lanzhou Gansu 730070, China
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Abstract

The paper investigated the exact controllability of delayed fractional evolution systems of order α ∈ ( 1 , 2 ) in abstract spaces. At first, the exact controllability result is obtained when the nonlinear term f is locally Lipschitz continuous. Then, the certain compactness conditions and the measure of noncompactness conditions were applied to demonstrate the exact controllability of the concerned problem. The discussion was based on the fixed point theorems and the cosine family theory.

Keywords

the cosine family theoryexact controllabilityfractional evolution equationsfixed point theorem
CLC number: 34K30, 34K35, 93C25

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AIMS Mathematics
Volume 9 Issue 7,
July 2024
Pages 17971-17983
DOI: 10.3934/math.2024875

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Cite this article:
Qin L. On the controllability results of semilinear delayed evolution systems involving fractional derivatives in Banach spaces. AIMS Mathematics, 2024, 9(7): 17971-17983. https://doi.org/10.3934/math.2024875

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Received: 02 March 2024
Revised: 04 May 2024
Accepted: 06 May 2024
Published: 15 July 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)