Existence and optimal control of Hilfer fractional evolution equations
This article investigates the existence and optimal controls for a class of Hilfer fractional evolution equations of order in (0,1)\left(0,1) with type of [0,10,1]. The first part focuses on analyzing the existence and uniqueness of the mild solution using the fixed point theorem and semigroup theor...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-01-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2024-0093 |
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| _version_ | 1832570457574866944 |
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| author | Zhou Mian Zhou Yong He Jia Wei Liang Yong |
| author_facet | Zhou Mian Zhou Yong He Jia Wei Liang Yong |
| author_sort | Zhou Mian |
| collection | DOAJ |
| description | This article investigates the existence and optimal controls for a class of Hilfer fractional evolution equations of order in (0,1)\left(0,1) with type of [0,10,1]. The first part focuses on analyzing the existence and uniqueness of the mild solution using the fixed point theorem and semigroup theory. In the second part, an optimal control problem that admits an optimal pair is considered. Furthermore, the necessary optimality conditions for an optimal control problem governed by semilinear fractional diffusion equations are presented. |
| format | Article |
| id | doaj-art-c218e9fcbc664c07ae7824e7deb720b2 |
| institution | Kabale University |
| issn | 2391-4661 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj-art-c218e9fcbc664c07ae7824e7deb720b22025-02-02T15:45:17ZengDe GruyterDemonstratio Mathematica2391-46612025-01-0158126227210.1515/dema-2024-0093Existence and optimal control of Hilfer fractional evolution equationsZhou Mian0Zhou Yong1He Jia Wei2Liang Yong3Faculty of Innovation Engineering, Macau University of Science and Technology, Macau 999078, ChinaFaculty of Innovation Engineering, Macau University of Science and Technology, Macau 999078, ChinaCollege of Mathematics and Information Science, Guangxi University, Nanning 530004, ChinaFaculty of Innovation Engineering, Macau University of Science and Technology, Macau 999078, ChinaThis article investigates the existence and optimal controls for a class of Hilfer fractional evolution equations of order in (0,1)\left(0,1) with type of [0,10,1]. The first part focuses on analyzing the existence and uniqueness of the mild solution using the fixed point theorem and semigroup theory. In the second part, an optimal control problem that admits an optimal pair is considered. Furthermore, the necessary optimality conditions for an optimal control problem governed by semilinear fractional diffusion equations are presented.https://doi.org/10.1515/dema-2024-0093existenceuniquenessoptimal controlfractional evolution equationshilfer derivative49j2049k2035r1126a33 |
| spellingShingle | Zhou Mian Zhou Yong He Jia Wei Liang Yong Existence and optimal control of Hilfer fractional evolution equations Demonstratio Mathematica existence uniqueness optimal control fractional evolution equations hilfer derivative 49j20 49k20 35r11 26a33 |
| title | Existence and optimal control of Hilfer fractional evolution equations |
| title_full | Existence and optimal control of Hilfer fractional evolution equations |
| title_fullStr | Existence and optimal control of Hilfer fractional evolution equations |
| title_full_unstemmed | Existence and optimal control of Hilfer fractional evolution equations |
| title_short | Existence and optimal control of Hilfer fractional evolution equations |
| title_sort | existence and optimal control of hilfer fractional evolution equations |
| topic | existence uniqueness optimal control fractional evolution equations hilfer derivative 49j20 49k20 35r11 26a33 |
| url | https://doi.org/10.1515/dema-2024-0093 |
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