{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T19:55:40Z","timestamp":1785873340189,"version":"3.56.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T00:00:00Z","timestamp":1766016000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T00:00:00Z","timestamp":1766016000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1007\/s12190-025-02722-7","type":"journal-article","created":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T13:34:50Z","timestamp":1766064890000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Synchronization of Caputo-Hadamard fractional-order fuzzy neural networks with time delays and uncertain parameters"],"prefix":"10.1007","volume":"72","author":[{"given":"Jie","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9723-8546","authenticated-orcid":false,"given":"Hong-Li","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yong","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huacheng","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinde","family":"Cao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,12,18]]},"reference":[{"key":"2722_CR1","doi-asserted-by":"crossref","unstructured":"Deng, Z., Zhang, J., Yang, Z.: Quasi-uniform stability for fractional-order fuzzy neural networks with uncertain proportional delay. J. Appl. Math. Comput. 70, 639\u2013656 (2024)","DOI":"10.1007\/s12190-023-01978-1"},{"key":"2722_CR2","doi-asserted-by":"crossref","unstructured":"Luo, M., Jiang, Z., Tan, M.: Mean-square stability of stochastic Clifford-valued Cohen-Grossberg neural networks with variable coefficients and time-varying delays. Neurocomputing 625, 129500 (2025)","DOI":"10.1016\/j.neucom.2025.129500"},{"key":"2722_CR3","doi-asserted-by":"crossref","unstructured":"Chen, X., Zhang, H., Ye, R., Lu, Q., Cao, J.: Quasi-projective synchronization analysis of delayed Caputo-type BAM neural networks in the complex field, neural process. Lett. 55, 7469\u20137492 (2023)","DOI":"10.1007\/s11063-023-11269-2"},{"key":"2722_CR4","doi-asserted-by":"crossref","unstructured":"Yang, T., Yang, L., Wu, C., Chua, L.: Fuzzy cellular neural networks: theory. In: Proc. IEEE Int. Workshop Cellular Neural Netw. Appl, vol. 1, pp. 181\u2013186. (1996)","DOI":"10.1109\/CNNA.1996.566545"},{"key":"2722_CR5","doi-asserted-by":"crossref","unstructured":"Mani, P., Rajan, R., Shanmugam, L., Joo, Y.: Adaptive control for fractional order induced chaotic fuzzy cellular neural networks and its application to image encryption, Inf. Sci. 491, 74\u201389 (2019)","DOI":"10.1016\/j.ins.2019.04.007"},{"key":"2722_CR6","doi-asserted-by":"crossref","unstructured":"Yan, S., Gu, Z., Park, J., Xie, X.: Synchronization of delayed fuzzy neural networks with probabilistic communication delay and its application to image encryption. IEEE Trans. Fuzzy Syst. 31, 930\u2013940 (2022)","DOI":"10.1109\/TFUZZ.2022.3193757"},{"key":"2722_CR7","doi-asserted-by":"crossref","unstructured":"Zhao, F., Jian, J., Wang, B.: Finite-time synchronization of fractional-order delayed memristive fuzzy neural networks. Fuzzy Sets Syst. 467, 108578 (2023)","DOI":"10.1016\/j.fss.2023.108578"},{"key":"2722_CR8","doi-asserted-by":"crossref","unstructured":"Hu, W., Zhu, Q., Karimi, H.: Some improved Razumikhin stability criteria for impulsive stochastic delay differential. IEEE Trans. Autom. Control. 64, 5207\u20135213 (2019)","DOI":"10.1109\/TAC.2019.2911182"},{"key":"2722_CR9","doi-asserted-by":"publisher","first-page":"040202","DOI":"10.1088\/1674-1056\/ab7803","volume":"29","author":"C. Chen","year":"2020","unstructured":"Chen, C., Ding, Z., Li, S., Wang, L.: Finite-time mittag-leffler synchronization of fractional-order delayed memristive neural networks with parameters uncertainty and discontinuous activation functions. Chin. Phys. B 29, 040202 (2020)","journal-title":"Chin. Phys. B"},{"key":"2722_CR10","doi-asserted-by":"publisher","first-page":"129475","DOI":"10.1016\/j.neucom.2025.129475","volume":"626","author":"H. Pan","year":"2025","unstructured":"Pan, H., Huang, C., Cao, J., Liu, H.: Global mittag-leffler synchronization of discontinuous memristor-based fractional-order fuzzy inertial neural networks with mixed delays. Neurocomputing 626, 129475 (2025)","journal-title":"Neurocomputing"},{"key":"2722_CR11","doi-asserted-by":"publisher","first-page":"6798","DOI":"10.1109\/TCYB.2020.3027755","volume":"52","author":"P. Liu","year":"2020","unstructured":"Liu, P., Kong, M., Zeng, Z.: Projective synchronization analysis of fractional-order neural networks with mixed time delays. IEEE Trans. Cybern. 52, 6798\u20136808 (2020)","journal-title":"IEEE Trans. Cybern."},{"key":"2722_CR12","doi-asserted-by":"publisher","first-page":"4147","DOI":"10.1007\/s12190-025-02399-y","volume":"71","author":"M. Shakeel","year":"2025","unstructured":"Shakeel, M., Liu, X., Zhang, S., Tang, M.: Global exponential synchronization of chaotic neural networks via novel coupling matrix design. J. Appl. Math. Comput. 71, 4147\u20134168 (2025)","journal-title":"J. Appl. Math. Comput."},{"key":"2722_CR13","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/s40314-024-02903-3","volume":"43","author":"L. Wang","year":"2024","unstructured":"Wang, L., Xu, G.: Quasi-synchronization of fractional-order complex-value BAM neural networks with time delays and discontinuous activations. Comput. Appl. Math. 43, 391 (2024)","journal-title":"Comput. Appl. Math."},{"key":"2722_CR14","doi-asserted-by":"publisher","first-page":"1109","DOI":"10.1007\/s12190-024-02234-w","volume":"71","author":"S. Kathiresan","year":"2025","unstructured":"Kathiresan, S., Kashkynbayev, A., Mohanrasu, S., Rajan, R.: Synchronization of fuzzy reaction-diffusion neural networks via semi-intermittent hybrid control. J. Appl. Math. Comput. 71, 1109\u20131139 (2025)","journal-title":"J. Appl. Math. Comput."},{"key":"2722_CR15","doi-asserted-by":"publisher","first-page":"130537","DOI":"10.1016\/j.neucom.2025.130537","volume":"647","author":"J. Wang","year":"2025","unstructured":"Wang, J., Zhu, S.: Finite-time synchronization of delayed quaternion-valued neural networks by non-decomposition and improved two-step methods. Neurocomputing 647, 130537 (2025)","journal-title":"Neurocomputing"},{"key":"2722_CR16","volume-title":"Fractional Differential Equations","author":"I. Podlubny","year":"1999","unstructured":"Podlubny, I.: Fractional Differential Equations. Academic, New York (1999)"},{"key":"2722_CR17","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations","author":"K. Miller","year":"1993","unstructured":"Miller, K., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)"},{"key":"2722_CR18","doi-asserted-by":"publisher","first-page":"2279","DOI":"10.1109\/TNNLS.2020.2995718","volume":"32","author":"Y. Kao","year":"2020","unstructured":"Kao, Y., Li, Y., Park, J., Chen, X.: Mittag-leffler synchronization of delayed fractional memristor neural networks via adaptive control. IEEE Trans. Neural Netw. Learn. Syst. 32, 2279\u20132284 (2020)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"2722_CR19","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.fss.2021.11.004","volume":"443","author":"H. Li","year":"2022","unstructured":"Li, H., Hu, C., Zhang, L., Jiang, H., Cao, J.: Complete and finite-time synchronization of fractional-order fuzzy neural networks via nonlinear feedback control. Fuzzy Sets Syst. 443, 50\u201369 (2022)","journal-title":"Fuzzy Sets Syst."},{"key":"2722_CR20","doi-asserted-by":"crossref","unstructured":"Jarad, F., Abdeljawad, T., Baleanu, D.: Caputo-type modification of the hadamard fractional derivatives. Adv. Differ. Equ. 142 (2012)","DOI":"10.1186\/1687-1847-2012-142"},{"key":"2722_CR21","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1016\/j.chaos.2017.03.032","volume":"102","author":"R. Garra","year":"2017","unstructured":"Garra, R., Mainardi, F., Spada, G.: A generalization of the Lomnitz logarithmic creep law via hadamard fractional calculus. Chaos Solitons Fractals 102, 333\u2013338 (2017)","journal-title":"Chaos Solitons Fractals"},{"key":"2722_CR22","doi-asserted-by":"publisher","first-page":"109833","DOI":"10.1109\/ACCESS.2019.2933865","volume":"7","author":"G. Wang","year":"2019","unstructured":"Wang, G., Ren, X., Zhang, L., Ahmad, B.: Explicit iteration and unique positive solution for a Caputo-Hadamard fractional turbulent flow model. IEEE Access 7, 109833\u2013109839 (2019)","journal-title":"IEEE Access"},{"key":"2722_CR23","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1016\/j.matcom.2023.03.020","volume":"210","author":"M. Rhaima","year":"2023","unstructured":"Rhaima, M.: Ulam-hyers stability for an impulsive caputo-hadamard fractional neutral stochastic differential equations with infinite delay. Math. Comput. Simul. 210, 281\u2013295 (2023)","journal-title":"Math. Comput. Simul."},{"key":"2722_CR24","doi-asserted-by":"publisher","first-page":"2420","DOI":"10.1007\/s13540-022-00106-3","volume":"25","author":"B. He","year":"2022","unstructured":"He, B., Zhou, H., Kou, C.: Stability analysis of hadamard and caputo-hadamard fractional nonlinear systems without and with delay, Fract. Calc. Appl. Anal. 25, 2420\u20132445 (2022)","journal-title":"Calc. Appl. Anal."},{"key":"2722_CR25","volume-title":"Theory and Application of Fractional Differential Equations","author":"A. Kilbas","year":"2006","unstructured":"Kilbas, A., Srivastava, H., Trujillo, J.: Theory and Application of Fractional Differential Equations. Elsevier, New York (2006)"},{"key":"2722_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10915-019-01102-1","volume":"85","author":"C. Li","year":"2020","unstructured":"Li, C., Li, Z., Wang, Z.: Mathematical analysis and the local discontinuous Galerkin method for caputo-hadamard fractional partial differential equation. J. Sci. Comput. 85, 1\u201327 (2020)","journal-title":"J. Sci. Comput."},{"key":"2722_CR27","doi-asserted-by":"publisher","first-page":"107723","DOI":"10.1016\/j.aml.2021.107723","volume":"125","author":"B. He","year":"2022","unstructured":"He, B., Zhou, H.: Caputo-hadamard fractional halanay inequality. Appl. Math. Lett. 125, 107723 (2022)","journal-title":"Appl. Math. Lett."},{"key":"2722_CR28","doi-asserted-by":"crossref","unstructured":"Chen, B., Chen, J.: Global asymptotical omega-periodicity of a fractional-order non-autonomous neural networks. Neural Netw. 68, 78\u201388 (2015)","DOI":"10.1016\/j.neunet.2015.04.006"},{"key":"2722_CR29","doi-asserted-by":"crossref","unstructured":"Du, F., Lu, J.: Finite-time synchronization of fractional-order delayed fuzzy cellular neural networks with parameter uncertainties. IEEE Trans. Fuzzy Syst. 31, 1769\u20131779 (2022)","DOI":"10.1109\/TFUZZ.2022.3214070"},{"key":"2722_CR30","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1016\/j.matcom.2021.08.001","volume":"191","author":"M. Shafiya","year":"2022","unstructured":"Shafiya, M., Nagamani, G., Dafik, D.: Global synchronization of uncertain fractional-order BAM neural networks with time delay via improved fractional-order integral inequality. Math. Comput. Simul. 191, 168\u2013186 (2022)","journal-title":"Math. Comput. Simul."},{"key":"2722_CR31","doi-asserted-by":"publisher","first-page":"968","DOI":"10.1109\/TFUZZ.2021.3051308","volume":"30","author":"J. Xiao","year":"2021","unstructured":"Xiao, J., Cheng, J., Shi, K., Zhang, R.: A general approach to fixed-time synchronization problem for fractional-order multidimension-valued fuzzy neural networks based on memristor. IEEE Trans. Fuzzy Syst. 30, 968\u2013977 (2021)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"2722_CR32","first-page":"1954","volume":"51","author":"Y. Zhou","year":"2019","unstructured":"Zhou, Y., Zhang, H., Zeng, Z.: Quasi-synchronization of delayed memristive neural networks via a hybrid impulsive control. IEEE Trans. Syst. Man Cybern. Syst. 51, 1954\u20131965 (2019)","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"2722_CR33","doi-asserted-by":"publisher","first-page":"880","DOI":"10.1109\/81.538999","volume":"43","author":"T. Yang","year":"1996","unstructured":"Yang, T., Yang, L.: The global stability of fuzzy cellular neural network. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 43, 880\u2013883 (1996)","journal-title":"IEEE Trans. Circuits Syst. I: Fundam. Theory Appl."},{"key":"2722_CR34","doi-asserted-by":"crossref","unstructured":"Xiao, J., Wen, S., Yang, X., Zhong, S.: New approach to global mittag-leffler synchronization problem of fractional-order quaternion-valued BAM neural networks based on a new inequality. Neural Netw. 122, 320\u2013337 (2020)","DOI":"10.1016\/j.neunet.2019.10.017"},{"key":"2722_CR35","doi-asserted-by":"crossref","unstructured":"Peng, Q., Jian, J.: Synchronization analysis of fractional-order inertial-type neural networks with time delays. Math. Comput. Simul. 205, 62\u201377 (2023)","DOI":"10.1016\/j.matcom.2022.09.023"},{"key":"2722_CR36","doi-asserted-by":"crossref","unstructured":"Yang, J., Li, H., Yang, J., Zhang, L., Jiang, H.: Quasi-synchronization and complete synchronization of fractional-order fuzzy BAM neural networks via nonlinear control, neural process. Lett. 54, 3303\u20133319 (2022)","DOI":"10.1007\/s11063-022-10769-x"},{"key":"2722_CR37","doi-asserted-by":"crossref","unstructured":"Du, F., Lu, J., Zhang, Q.: Practical finite-time synchronization of delayed fuzzy cellular neural networks with fractional-order, Inf. Sci. 667, 120457 (2024)","DOI":"10.1016\/j.ins.2024.120457"},{"key":"2722_CR38","doi-asserted-by":"crossref","unstructured":"Yang, X., Zhu, Q., Wang, H.: Exponential stabilization of stochastic systems via novel event-triggered switching controls. IEEE Trans. Autom. Control. 69, 7948\u20137955 (2024)","DOI":"10.1109\/TAC.2024.3406668"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-025-02722-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-025-02722-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-025-02722-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T16:46:58Z","timestamp":1767890818000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-025-02722-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,18]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["2722"],"URL":"https:\/\/doi.org\/10.1007\/s12190-025-02722-7","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,18]]},"assertion":[{"value":"29 July 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 October 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 November 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 December 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declaration"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interest"}}],"article-number":"56"}}