Optimal Control for <i>k</i> × <i>k</i> Cooperative Fractional Systems
This paper discusses the optimal control issue for elliptic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>×</mo><mi>k</mi></mrow></semantics>...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/10/559 |
| _version_ | 1797473204468449280 |
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| author | Hassan M. Serag Abd-Allah Hyder Mahmoud El-Badawy Areej A. Almoneef |
| author_facet | Hassan M. Serag Abd-Allah Hyder Mahmoud El-Badawy Areej A. Almoneef |
| author_sort | Hassan M. Serag |
| collection | DOAJ |
| description | This paper discusses the optimal control issue for elliptic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>×</mo><mi>k</mi></mrow></semantics></math></inline-formula> cooperative fractional systems. The fractional operators are proposed in the Laplace sense. Because of the nonlocality of the Laplace fractional operators, we reformulate the issue as an extended issue on a semi-infinite cylinder in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula>. The weak solution for these fractional systems is then proven to exist and be unique. Moreover, the existence and optimality conditions can be inferred as a consequence. |
| first_indexed | 2024-03-09T20:11:31Z |
| format | Article |
| id | doaj.art-4645be9f458e48cf89f61793aef35b57 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T20:11:31Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-4645be9f458e48cf89f61793aef35b572023-11-24T00:11:35ZengMDPI AGFractal and Fractional2504-31102022-10-0161055910.3390/fractalfract6100559Optimal Control for <i>k</i> × <i>k</i> Cooperative Fractional SystemsHassan M. Serag0Abd-Allah Hyder1Mahmoud El-Badawy2Areej A. Almoneef3Department of Mathematics, Faculty of Sciences, Al-Azhar University, Cairo 71524, EgyptDepartment of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi ArabiaDepartment of Mathematics, Faculty of Sciences, Al-Azhar University, Cairo 71524, EgyptDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaThis paper discusses the optimal control issue for elliptic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>×</mo><mi>k</mi></mrow></semantics></math></inline-formula> cooperative fractional systems. The fractional operators are proposed in the Laplace sense. Because of the nonlocality of the Laplace fractional operators, we reformulate the issue as an extended issue on a semi-infinite cylinder in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula>. The weak solution for these fractional systems is then proven to exist and be unique. Moreover, the existence and optimality conditions can be inferred as a consequence.https://www.mdpi.com/2504-3110/6/10/559nonlocal operatorfractional laplace operatorweak solutionoptimality conditionscooperative systems |
| spellingShingle | Hassan M. Serag Abd-Allah Hyder Mahmoud El-Badawy Areej A. Almoneef Optimal Control for <i>k</i> × <i>k</i> Cooperative Fractional Systems Fractal and Fractional nonlocal operator fractional laplace operator weak solution optimality conditions cooperative systems |
| title | Optimal Control for <i>k</i> × <i>k</i> Cooperative Fractional Systems |
| title_full | Optimal Control for <i>k</i> × <i>k</i> Cooperative Fractional Systems |
| title_fullStr | Optimal Control for <i>k</i> × <i>k</i> Cooperative Fractional Systems |
| title_full_unstemmed | Optimal Control for <i>k</i> × <i>k</i> Cooperative Fractional Systems |
| title_short | Optimal Control for <i>k</i> × <i>k</i> Cooperative Fractional Systems |
| title_sort | optimal control for i k i i k i cooperative fractional systems |
| topic | nonlocal operator fractional laplace operator weak solution optimality conditions cooperative systems |
| url | https://www.mdpi.com/2504-3110/6/10/559 |
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