Global Mittag-Leffler Synchronization of Fractional-Order Fuzzy Inertia Neural Networks with Reaction–Diffusion Terms Under Boundary Control
This study is devoted to solving the global Mittag-Leffler synchronization problem of fractional-order fuzzy reaction–diffusion inertial neural networks by using boundary control. Firstly, the considered network model incorporates the inertia term, reaction–diffusion term and fuzzy logic, thereby en...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/7/405 |
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| author | Lianyang Hu Haijun Jiang Cheng Hu Yue Ren Lvming Liu Xuejiao Qin |
| author_facet | Lianyang Hu Haijun Jiang Cheng Hu Yue Ren Lvming Liu Xuejiao Qin |
| author_sort | Lianyang Hu |
| collection | DOAJ |
| description | This study is devoted to solving the global Mittag-Leffler synchronization problem of fractional-order fuzzy reaction–diffusion inertial neural networks by using boundary control. Firstly, the considered network model incorporates the inertia term, reaction–diffusion term and fuzzy logic, thereby enhancing the existing model framework. Secondly, to prevent an increase in the number of state variables due to the reduced-order approach, a non-reduced-order method is fully utilized. Additionally, a boundary controller is designed to lower resource usage. Subsequently, under the Neumann boundary condition, the mixed boundary condition and the Robin boundary condition, three synchronization conditions are established with the help of the non-reduced-order approach and LMI technique, respectively. Lastly, two numerical examples are offered to verify the reliability of the theoretical results and the availability of the boundary controller through MATLAB simulations. |
| format | Article |
| id | doaj-art-8b20888cd98c488fbf7e4c7bf6815c58 |
| institution | DOAJ |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-8b20888cd98c488fbf7e4c7bf6815c582025-08-20T03:07:58ZengMDPI AGFractal and Fractional2504-31102025-06-019740510.3390/fractalfract9070405Global Mittag-Leffler Synchronization of Fractional-Order Fuzzy Inertia Neural Networks with Reaction–Diffusion Terms Under Boundary ControlLianyang Hu0Haijun Jiang1Cheng Hu2Yue Ren3Lvming Liu4Xuejiao Qin5College of Mathematics and System Science, Xinjiang University, Urumqi 830017, ChinaCollege of Mathematics and System Science, Xinjiang University, Urumqi 830017, ChinaCollege of Mathematics and System Science, Xinjiang University, Urumqi 830017, ChinaCollege of Mathematics and System Science, Xinjiang University, Urumqi 830017, ChinaCollege of Mathematics and System Science, Xinjiang University, Urumqi 830017, ChinaSchool of Biomedical Engineering, Xinjiang Second Medical College, Karamay 834000, ChinaThis study is devoted to solving the global Mittag-Leffler synchronization problem of fractional-order fuzzy reaction–diffusion inertial neural networks by using boundary control. Firstly, the considered network model incorporates the inertia term, reaction–diffusion term and fuzzy logic, thereby enhancing the existing model framework. Secondly, to prevent an increase in the number of state variables due to the reduced-order approach, a non-reduced-order method is fully utilized. Additionally, a boundary controller is designed to lower resource usage. Subsequently, under the Neumann boundary condition, the mixed boundary condition and the Robin boundary condition, three synchronization conditions are established with the help of the non-reduced-order approach and LMI technique, respectively. Lastly, two numerical examples are offered to verify the reliability of the theoretical results and the availability of the boundary controller through MATLAB simulations.https://www.mdpi.com/2504-3110/9/7/405fractional-order fuzzy inertia neural networkreaction–diffusionglobal Mittag-Leffler synchronizationboundary control |
| spellingShingle | Lianyang Hu Haijun Jiang Cheng Hu Yue Ren Lvming Liu Xuejiao Qin Global Mittag-Leffler Synchronization of Fractional-Order Fuzzy Inertia Neural Networks with Reaction–Diffusion Terms Under Boundary Control Fractal and Fractional fractional-order fuzzy inertia neural network reaction–diffusion global Mittag-Leffler synchronization boundary control |
| title | Global Mittag-Leffler Synchronization of Fractional-Order Fuzzy Inertia Neural Networks with Reaction–Diffusion Terms Under Boundary Control |
| title_full | Global Mittag-Leffler Synchronization of Fractional-Order Fuzzy Inertia Neural Networks with Reaction–Diffusion Terms Under Boundary Control |
| title_fullStr | Global Mittag-Leffler Synchronization of Fractional-Order Fuzzy Inertia Neural Networks with Reaction–Diffusion Terms Under Boundary Control |
| title_full_unstemmed | Global Mittag-Leffler Synchronization of Fractional-Order Fuzzy Inertia Neural Networks with Reaction–Diffusion Terms Under Boundary Control |
| title_short | Global Mittag-Leffler Synchronization of Fractional-Order Fuzzy Inertia Neural Networks with Reaction–Diffusion Terms Under Boundary Control |
| title_sort | global mittag leffler synchronization of fractional order fuzzy inertia neural networks with reaction diffusion terms under boundary control |
| topic | fractional-order fuzzy inertia neural network reaction–diffusion global Mittag-Leffler synchronization boundary control |
| url | https://www.mdpi.com/2504-3110/9/7/405 |
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