{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T23:44:14Z","timestamp":1774395854217,"version":"3.50.1"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T00:00:00Z","timestamp":1738886400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T00:00:00Z","timestamp":1738886400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100019904","name":"Vellore Institute of Technology, Chennai","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100019904","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Process Lett"],"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>In this paper, a hybrid controller with a sampled data control is investigated to achieve finite-time master\u2013slave synchronization of delayed fractional-order neural networks (DFONNs). A Lyapunov-Krasovskii functional is constructed to obtain the sufficient conditions that incorporate delay information. For the first time, the asymptotic stability of the error system is guaranteed in a finite-time using the inequality technique and a sampled-data hybrid controller. The obtained conditions are expressed via linear matrix inequality. Notably, the proposed approach outperforms existing methods, demonstrating improved results in a comparative analysis. An explicit formula is utilized to calculate the settling time, which is significantly influenced by the fractional order <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$0&lt;\\beta \\le 1$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mn>0<\/mml:mn>\n                    <mml:mo>&lt;<\/mml:mo>\n                    <mml:mi>\u03b2<\/mml:mi>\n                    <mml:mo>\u2264<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>. The superior performance of the proposed control method is evident, showcasing its effectiveness through numerical simulations and addressing the synchronization problem in DFONNs.<\/jats:p>","DOI":"10.1007\/s11063-025-11733-1","type":"journal-article","created":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T20:13:18Z","timestamp":1738959198000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Master\u2013Slave Finite-Time Synchronization of Chaotic Fractional-Order Neural Networks under Hybrid Sampled-Data Control: An LMI Approach"],"prefix":"10.1007","volume":"57","author":[{"given":"R.","family":"Kiruthika","sequence":"first","affiliation":[]},{"given":"A.","family":"Manivannan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,2,7]]},"reference":[{"issue":"21","key":"11733_CR1","first-page":"1021","volume":"4","author":"Mehdi Dalir","year":"2010","unstructured":"Dalir Mehdi, Bashour Majid (2010) Applications of fractional calculus. Appl Math Sci 4(21):1021\u20131032","journal-title":"Appl Math Sci"},{"key":"11733_CR2","unstructured":"Baleanu Dumitru, Balas Valentina\u00a0Emilia, Agarwal Praveen (2022) Fractional order systems and applications in engineering. Academic Press"},{"issue":"5","key":"11733_CR3","doi-asserted-by":"publisher","first-page":"1305","DOI":"10.1016\/j.chaos.2006.07.051","volume":"36","author":"Wei-Ching Chen","year":"2008","unstructured":"Chen Wei-Ching (2008) Nonlinear dynamics and chaos in a fractional-order financial system. Chaos, Solit Fract 36(5):1305\u20131314","journal-title":"Chaos, Solit Fract"},{"issue":"07","key":"11733_CR4","doi-asserted-by":"publisher","first-page":"1527","DOI":"10.1142\/S0218127498001170","volume":"8","author":"P Arena","year":"1998","unstructured":"Arena P, Caponetto R, Fortuna L, Porto D (1998) Bifurcation and chaos in noninteger order cellular neural networks. Int J Bifurcat Chaos 8(07):1527\u20131539","journal-title":"Int J Bifurcat Chaos"},{"key":"11733_CR5","doi-asserted-by":"crossref","unstructured":"Roohi Majid, Zhang Chongqi, Chen Yucheng (2020) Adaptive model-free synchronization of different fractional-order neural networks with an application in cryptography. Nonlinear Dyn 100:3979\u20134001","DOI":"10.1007\/s11071-020-05719-y"},{"key":"11733_CR6","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2020.110576","volume":"144","author":"Xiong Pei-Ying","year":"2021","unstructured":"Pei-Ying Xiong, Hadi Jahanshahi, Ra\u00fal Alcaraz, Yu-Ming Chu, G\u00f3mez-Aguilar JF, Alsaadi Fawaz E (2021) Spectral entropy analysis and synchronization of a multi-stable fractional-order chaotic system using a novel neural network-based chattering-free sliding mode technique. Chaos, Solit Fract 144:110576","journal-title":"Chaos, Solit Fract"},{"key":"11733_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijepes.2023.109746","volume":"156","author":"M AbdelAty Amr","year":"2024","unstructured":"AbdelAty Amr M, Ahmed Al-Durra, Hatem Zeineldin, El-Saadany Ehab F (2024) Improving small-signal stability of inverter-based microgrids using fractional-order control. Int J Electrical Power Energy Syst 156:109746","journal-title":"Int J Electrical Power Energy Syst"},{"key":"11733_CR8","doi-asserted-by":"crossref","unstructured":"Muhammad Ibrahim Malik, Ahmad Kamran Muhammad, Naeem Mannan Malik Muhammad, Hyo Jung Il, Sangil Kim (2021) Lag synchronization of coupled time-delayed Fitzhugh-Nagumo neural networks via feedback control. Sci Rep 11(1):3884","DOI":"10.1038\/s41598-021-82886-x"},{"key":"11733_CR9","doi-asserted-by":"crossref","unstructured":"Jahanshahi Hadi, Yousefpour Amin, Munoz-Pacheco Jesus\u00a0M , Kacar Sezgin, Pham Viet-Thanh, Alsaadi Fawaz\u00a0E (2020) A new fractional-order hyperchaotic memristor oscillator: Dynamic analysis, robust adaptive synchronization, and its application to voice encryption. Appl Math Comput, 383:125310","DOI":"10.1016\/j.amc.2020.125310"},{"issue":"17","key":"11733_CR10","doi-asserted-by":"publisher","first-page":"13648","DOI":"10.1016\/j.jfranklin.2022.04.036","volume":"360","author":"Wang Bo","year":"2023","unstructured":"Bo Wang, Hadi Jahanshahi, Burak Ar\u0131c\u0131o\u011flu, Bar\u0131\u015f Boru, Sezgin Kacar, Alotaibi Naif D (2023) A variable-order fractional neural network: Dynamical properties, data security application, and synchronization using a novel control algorithm with a finite-time estimator. J Franklin Inst 360(17):13648\u201313670","journal-title":"J Franklin Inst"},{"key":"11733_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2024.106124","volume":"172","author":"Xin Liu","year":"2024","unstructured":"Liu Xin, Chen Lili, Zhao Yanfeng, Li Honglin (2024) Event-triggered hybrid impulsive control for synchronization of fractional-order multilayer signed networks under cyber attacks. Neural Netw 172:106124","journal-title":"Neural Netw"},{"issue":"8","key":"11733_CR12","doi-asserted-by":"publisher","first-page":"11173","DOI":"10.1007\/s11063-023-11371-5","volume":"55","author":"Jianying Xiao","year":"2023","unstructured":"Xiao Jianying, Guo Xiao, Li Yongtao, Wen Shiping (2023) Further research on the problems of synchronization for fractional-order BAM neural networks in octonion-valued domain. Neural Process Lett 55(8):11173\u201311208","journal-title":"Neural Process Lett"},{"issue":"10","key":"11733_CR13","doi-asserted-by":"publisher","first-page":"6223","DOI":"10.1002\/mma.6367","volume":"43","author":"Anbalagan Pratap","year":"2020","unstructured":"Pratap Anbalagan, Raja Ramachandran, Alzabut Jehad, Cao Jinde, Rajchakit Grienggrai, Huang Chuangxia (2020) Mittag-leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field. Math Methods Appl Sci 43(10):6223\u20136253","journal-title":"Math Methods Appl Sci"},{"key":"11733_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2023.113790","volume":"174","author":"Shasha Wang","year":"2023","unstructured":"Wang Shasha, Jian Jigui (2023) Predefined-time synchronization of fractional-order memristive competitive neural networks with time-varying delays. Chaos, Solit Fract 174:113790","journal-title":"Chaos, Solit Fract"},{"issue":"2","key":"11733_CR15","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/ad1867","volume":"99","author":"AAH Shoreh","year":"2024","unstructured":"Shoreh AAH, Mahmoud Gamal M (2024) A novel adaptive synchronization algorithm for a general class of fractional-order complex-valued systems with unknown parameters, and applications to circuit realization and color image encryption. Phys Scripta 99(2):025212","journal-title":"Phys Scripta"},{"issue":"3","key":"11733_CR16","doi-asserted-by":"publisher","first-page":"1671","DOI":"10.1109\/TCYB.2023.3237248","volume":"54","author":"Chen Wei","year":"2023","unstructured":"Wei Chen, Wang Xiaoping, Hui Meng, Zeng Zhigang (2023) Quasi-synchronization of fractional multiweighted coupled neural networks via aperiodic intermittent control. IEEE Trans Cybernetics 54(3):1671\u20131684","journal-title":"IEEE Trans Cybernetics"},{"issue":"5","key":"11733_CR17","doi-asserted-by":"publisher","first-page":"6657","DOI":"10.1007\/s11063-023-11153-z","volume":"55","author":"Xu Yingying","year":"2023","unstructured":"Yingying Xu, Li Hong-Li, Zhang Long, Cheng Hu, Jiang Haijun (2023) Quasi-projective and Mittag-Leffler synchronization of discrete-time fractional-order complex-valued fuzzy neural networks. Neural Process Lett 55(5):6657\u20136677","journal-title":"Neural Process Lett"},{"issue":"4","key":"11733_CR18","doi-asserted-by":"publisher","first-page":"3263","DOI":"10.1016\/j.jfranklin.2023.01.024","volume":"360","author":"Mingfang Zhao","year":"2023","unstructured":"Zhao Mingfang, Li Hong-Li, Zhang Long, Cheng Hu, Jiang Haijun (2023) Quasi-projective synchronization of discrete-time fractional-order quaternion-valued neural networks. J Franklin Inst 360(4):3263\u20133279","journal-title":"J Franklin Inst"},{"key":"11733_CR19","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1016\/j.isatra.2022.10.046","volume":"136","author":"Wu Xiang","year":"2023","unstructured":"Xiang Wu, Liu Shutang, Wang Huiyu, Wang Yin (2023) Stability and pinning synchronization of delayed memristive neural networks with fractional-order and reaction-diffusion terms. ISA Trans 136:114\u2013125","journal-title":"ISA Trans"},{"key":"11733_CR20","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1007\/s00521-015-1876-1","volume":"27","author":"Liping Chen","year":"2016","unstructured":"Chen Liping, Liu Cong, Ranchao Wu, He Yigang, Chai Yi (2016) Finite-time stability criteria for a class of fractional-order neural networks with delay. Neural Comput Appl 27:549\u2013556","journal-title":"Neural Comput Appl"},{"key":"11733_CR21","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.neunet.2017.06.011","volume":"94","author":"Xiao Peng","year":"2017","unstructured":"Peng Xiao, Huaiqin Wu, Song Ka, Shi Jiaxin (2017) Global synchronization in finite time for fractional-order neural networks with discontinuous activations and time delays. Neural Netw 94:46\u201354","journal-title":"Neural Netw"},{"key":"11733_CR22","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1016\/j.neucom.2018.08.003","volume":"316","author":"Xiaofan Li","year":"2018","unstructured":"Li Xiaofan, Fang Jian-an, Zhang Wenbing, Li Huiyuan (2018) Finite-time synchronization of fractional-order memristive recurrent neural networks with discontinuous activation functions. Neurocomputing 316:284\u2013293","journal-title":"Neurocomputing"},{"issue":"1","key":"11733_CR23","doi-asserted-by":"publisher","first-page":"12545","DOI":"10.1038\/s41598-023-37737-2","volume":"13","author":"Brahmi Hajer","year":"2023","unstructured":"Hajer Brahmi, Boudour Ammar, Amel Ksibi, Farouk Cherif, Ghadah Aldehim, Alimi Adel M (2023) Finite-time complete periodic synchronization of memristive neural networks with mixed delays. Sci Rep 13(1):12545","journal-title":"Sci Rep"},{"key":"11733_CR24","doi-asserted-by":"publisher","first-page":"910","DOI":"10.1016\/j.matcom.2022.07.028","volume":"203","author":"Zhanying Yang","year":"2023","unstructured":"Yang Zhanying, Zhang Jie, Zhang Zhihui, Mei Jun (2023) An improved criterion on finite-time stability for fractional-order fuzzy cellular neural networks involving leakage and discrete delays. Math Comput Simulat 203:910\u2013925","journal-title":"Math Comput Simulat"},{"key":"11733_CR25","doi-asserted-by":"crossref","unstructured":"Si Xindong, Wang Zhen, Fan Yingjie (2023) Quantized control for finite-time synchronization of delayed fractional-order memristive neural networks: The Gronwall inequality approach. Exp Syst Appl 215:119310","DOI":"10.1016\/j.eswa.2022.119310"},{"key":"11733_CR26","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/j.neucom.2018.09.021","volume":"320","author":"Hong-Li Li","year":"2018","unstructured":"Li Hong-Li, Cao Jinde, Jiang Haijun, Alsaedi Ahmed (2018) Finite-time synchronization of fractional-order complex networks via hybrid feedback control. Neurocomputing 320:69\u201375","journal-title":"Neurocomputing"},{"key":"11733_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2022.106822","volume":"116","author":"Hui Meng","year":"2023","unstructured":"Meng Hui, Chen Wei, Zhang Jiao Iu, Ho-Ching Herbert, Rui Yao, Lin Bai (2023) Finite-time synchronization of fractional-order memristive neural networks via feedback and periodically intermittent control. Commun Nonlinear Sci Numerical Simulation 116:106822","journal-title":"Commun Nonlinear Sci Numerical Simulation"},{"key":"11733_CR28","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.fss.2021.11.004","volume":"443","author":"Hong-Li Li","year":"2022","unstructured":"Li Hong-Li, Cheng Hu, Zhang Long, Jiang Haijun, Cao Jinde (2022) Complete and finite-time synchronization of fractional-order fuzzy neural networks via nonlinear feedback control. Fuzzy Sets Syst 443:50\u201369","journal-title":"Fuzzy Sets Syst"},{"key":"11733_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.neunet.2020.02.004","volume":"126","author":"Yuanhua Qiao","year":"2020","unstructured":"Qiao Yuanhua, Yan Hongyun, Duan Lijuan, Miao Jun (2020) Finite-time synchronization of fractional-order gene regulatory networks with time delay. Neural Netw 126:1\u201310","journal-title":"Neural Netw"},{"key":"11733_CR30","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1016\/j.neucom.2017.05.075","volume":"266","author":"Dasong Huang","year":"2017","unstructured":"Huang Dasong, Jiang Minghui, Jian Jigui (2017) Finite-time synchronization of inertial memristive neural networks with time-varying delays via sampled-date control. Neurocomputing 266:527\u2013539","journal-title":"Neurocomputing"},{"key":"11733_CR31","unstructured":"Podlubny Igor (1998) Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier"},{"key":"11733_CR32","doi-asserted-by":"crossref","unstructured":"Duarte-Mermoud Manuel A, Norelys Aguila-Camacho, Gallegos Javier A, Rafael Castro-Linares (2015) Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Commun Nonlinear Sci Numerical Simulation 22(1\u20133):650\u2013659","DOI":"10.1016\/j.cnsns.2014.10.008"},{"key":"11733_CR33","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2023.113252","volume":"169","author":"R Kiruthika","year":"2023","unstructured":"Kiruthika R, Krishnasamy R, Lakshmanan S, Prakash M, Manivannan A (2023) Non-fragile sampled-data control for synchronization of chaotic fractional-order delayed neural networks via LMI approach. Chaos, Solit Fract 169:113252","journal-title":"Chaos, Solit Fract"},{"issue":"11","key":"11733_CR34","doi-asserted-by":"publisher","first-page":"3631","DOI":"10.1016\/j.apm.2010.03.012","volume":"34","author":"Xinsong Yang","year":"2010","unstructured":"Yang Xinsong, Cao Jinde (2010) Finite-time stochastic synchronization of complex networks. Appl Math Model 34(11):3631\u20133641","journal-title":"Appl Math Model"},{"key":"11733_CR35","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1016\/j.neucom.2014.07.060","volume":"149","author":"Wu Ranchao","year":"2015","unstructured":"Ranchao Wu, Yanfen Lu, Chen Liping (2015) Finite-time stability of fractional delayed neural networks. Neurocomputing 149:700\u2013707","journal-title":"Neurocomputing"},{"key":"11733_CR36","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.neucom.2014.11.023","volume":"152","author":"Xujun Yang","year":"2015","unstructured":"Yang Xujun, Song Qiankun, Liu Yurong, Zhao Zhenjiang (2015) Finite-time stability analysis of fractional-order neural networks with delay. Neurocomputing 152:19\u201326","journal-title":"Neurocomputing"},{"issue":"11","key":"11733_CR37","doi-asserted-by":"publisher","first-page":"3584","DOI":"10.1007\/s12555-021-0529-7","volume":"20","author":"Xu Mei","year":"2022","unstructured":"Mei Xu, Ding Yucai (2022) Fixed-time synchronization of fractional-order Hopfield neural networks. Int J Control, Autom Syst 20(11):3584\u20133591","journal-title":"Int J Control, Autom Syst"}],"container-title":["Neural Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-025-11733-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11063-025-11733-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-025-11733-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T12:47:15Z","timestamp":1741697235000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11063-025-11733-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,7]]},"references-count":37,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["11733"],"URL":"https:\/\/doi.org\/10.1007\/s11063-025-11733-1","relation":{},"ISSN":["1573-773X"],"issn-type":[{"value":"1573-773X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,7]]},"assertion":[{"value":"21 January 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 February 2025","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"15"}}