Finite-Approximate Controllability of -Caputo Fractional Systems

This paper introduces a methodology for examining finite-approximate controllability in Hilbert spaces for linear/semilinear ν -Caputo fractional evolution equations. A novel criterion for achieving finite-approximate controllability in linear ν -Caputo fractional evolution equations is established,...

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Bibliographic Details
Published in:Fractal and fractional 2023-12, Vol.8 (1), p.21
Main Authors: Muath Awadalla, Nazim I. Mahmudov, Jihan Alahmadi
Format: Article
Language:English
Subjects:
<named-content content-type="inline-formula"> <mml:math id="mm1001"> ν </mml:math> </named-content>-caputo fractional system
controllability
fixed point theorems
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Summary:This paper introduces a methodology for examining finite-approximate controllability in Hilbert spaces for linear/semilinear ν -Caputo fractional evolution equations. A novel criterion for achieving finite-approximate controllability in linear ν -Caputo fractional evolution equations is established, utilizing resolvent-like operators. Additionally, we identify a control strategy that not only satisfies the approximative controllability property but also ensures exact finite-dimensional controllability. Leveraging the approximative controllability of the corresponding linear ν -Caputo fractional evolution system, we establish sufficient conditions for achieving finite-approximative controllability in the semilinear ν -Caputo fractional evolution equation. These findings extend and build upon recent advancements in this field. The paper also explores applications to ν -Caputo fractional heat equations.
ISSN:2504-3110
DOI:10.3390/fractalfract8010021