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Research Article | Open Access

Study on the controllability of delayed evolution inclusions involving fractional derivatives

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

This paper dealt with the infinite controllability of delayed evolution inclusions with α-order fractional derivatives in Fr e ´ chet spaces, where α ∈ ( 1 , 2 ). The controllability conclusion was acquired without any compactness for the nonlinear term, the cosine family, and the sine family. The investigation was based on a nonlinear alternative and the cosine family theory. An application of our findings was provided.

Keywords

fractional evolution inclusionsinfinite controllabilitythe cosine familyfréchet spacesmild solutions
CLC number: 34K35, 93C25

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AIMS Mathematics
Volume 9 Issue 7,
July 2024
Pages 17984-17996
DOI: 10.3934/math.2024876

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Liang Y. Study on the controllability of delayed evolution inclusions involving fractional derivatives. AIMS Mathematics, 2024, 9(7): 17984-17996. https://doi.org/10.3934/math.2024876

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Received: 13 February 2024
Revised: 03 May 2024
Accepted: 08 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)