Finite-Approximate Controllability of <inline-formula><math display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo Fractional Systems
This paper introduces a methodology for examining finite-approximate controllability in Hilbert spaces for linear/semilinear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics><...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/1/21 |
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| author | Muath Awadalla Nazim I. Mahmudov Jihan Alahmadi |
| author_facet | Muath Awadalla Nazim I. Mahmudov Jihan Alahmadi |
| author_sort | Muath Awadalla |
| collection | DOAJ |
| description | This paper introduces a methodology for examining finite-approximate controllability in Hilbert spaces for linear/semilinear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo fractional evolution equations. A novel criterion for achieving finite-approximate controllability in linear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo fractional evolution system, we establish sufficient conditions for achieving finite-approximative controllability in the semilinear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo fractional evolution equation. These findings extend and build upon recent advancements in this field. The paper also explores applications to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo fractional heat equations. |
| first_indexed | 2024-03-08T10:55:15Z |
| format | Article |
| id | doaj.art-65a17c3a612b4d29b1c76304f21d1a15 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-08T10:55:15Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-65a17c3a612b4d29b1c76304f21d1a152024-01-26T16:35:14ZengMDPI AGFractal and Fractional2504-31102023-12-01812110.3390/fractalfract8010021Finite-Approximate Controllability of <inline-formula><math display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo Fractional SystemsMuath Awadalla0Nazim I. Mahmudov1Jihan Alahmadi2Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi ArabiaDepartment of Mathematics, Eastern Mediterranean University, Famagusta 99628, TurkeyDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaThis paper introduces a methodology for examining finite-approximate controllability in Hilbert spaces for linear/semilinear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo fractional evolution equations. A novel criterion for achieving finite-approximate controllability in linear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo fractional evolution system, we establish sufficient conditions for achieving finite-approximative controllability in the semilinear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo fractional evolution equation. These findings extend and build upon recent advancements in this field. The paper also explores applications to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo fractional heat equations.https://www.mdpi.com/2504-3110/8/1/21controllabilityfixed point theorems<named-content content-type="inline-formula"><inline-formula> <mml:math id="mm1001"> <mml:semantics> <mml:mi>ν</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-caputo fractional system |
| spellingShingle | Muath Awadalla Nazim I. Mahmudov Jihan Alahmadi Finite-Approximate Controllability of <inline-formula><math display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo Fractional Systems Fractal and Fractional controllability fixed point theorems <named-content content-type="inline-formula"><inline-formula> <mml:math id="mm1001"> <mml:semantics> <mml:mi>ν</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-caputo fractional system |
| title | Finite-Approximate Controllability of <inline-formula><math display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo Fractional Systems |
| title_full | Finite-Approximate Controllability of <inline-formula><math display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo Fractional Systems |
| title_fullStr | Finite-Approximate Controllability of <inline-formula><math display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo Fractional Systems |
| title_full_unstemmed | Finite-Approximate Controllability of <inline-formula><math display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo Fractional Systems |
| title_short | Finite-Approximate Controllability of <inline-formula><math display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-Caputo Fractional Systems |
| title_sort | finite approximate controllability of inline formula math display inline semantics mi ν mi semantics math inline formula caputo fractional systems |
| topic | controllability fixed point theorems <named-content content-type="inline-formula"><inline-formula> <mml:math id="mm1001"> <mml:semantics> <mml:mi>ν</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-caputo fractional system |
| url | https://www.mdpi.com/2504-3110/8/1/21 |
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