{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,28]],"date-time":"2026-05-28T00:26:59Z","timestamp":1779928019618,"version":"3.53.1"},"reference-count":26,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T00:00:00Z","timestamp":1766707200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007957","name":"Chongqing Municipal Education Commission","doi-asserted-by":"crossref","award":["KJQN202301318"],"award-info":[{"award-number":["KJQN202301318"]}],"id":[{"id":"10.13039\/501100007957","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100007957","name":"Chongqing Municipal Education Commission","doi-asserted-by":"crossref","award":["KJQN202401336"],"award-info":[{"award-number":["KJQN202401336"]}],"id":[{"id":"10.13039\/501100007957","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"crossref","award":["2024J08207"],"award-info":[{"award-number":["2024J08207"]}],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003410","name":"Fujian Provincial Department of Education","doi-asserted-by":"crossref","award":["JAT220213"],"award-info":[{"award-number":["JAT220213"]}],"id":[{"id":"10.13039\/501100003410","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper focuses on exploring the existence and uniqueness of solutions for a specific type of impulsive fractional-order complex-valued stochastic neural network within the complex domain, a topic hitherto undocumented. The combination of fractional order, stochastic nature, complex values, and impulses allows the model to seize memory-related, noise-resilient, phase-sensitive, and discontinuous dynamics. These dynamics are crucial for applications in neuroscience, signal processing, engineering control, and time-series prediction. In contrast to more simplistic models, this framework provides greater fidelity when simulating real-world systems and wider applicability without the need for redundant component splitting, thus justifying the requirement for such a comprehensive model. Leveraging the contraction mapping principle and contradiction, sufficient conditions are deduced to guarantee the existence and uniform stability (in the distribution sense) of solutions for the impulsive fractional-order complex-valued stochastic neural networks under study. Finally, a numerical example is presented to illustrate the feasibility and precision of our findings.<\/jats:p>","DOI":"10.3390\/axioms15010017","type":"journal-article","created":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T00:50:42Z","timestamp":1766969442000},"page":"17","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Investigating Uniform Stability of Fractional-Order Complex-Valued Stochastic Neural Networks with Impulses via a Direct Method"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6110-6269","authenticated-orcid":false,"given":"Jianglian","family":"Xiang","sequence":"first","affiliation":[{"name":"Department of Mathematics and Artificial Intelligence, Chongqing University of Arts and Sciences, Chongqing 402100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tiantian","family":"Tang","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Artificial Intelligence, Chongqing University of Arts and Sciences, Chongqing 402100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoli","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Minnan Normal University, Zhangzhou 363000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1109\/TIP.2017.2760518","article-title":"Deep neural networks for no-reference and full-reference image quality assessment","volume":"27","author":"Bosse","year":"2018","journal-title":"IEEE Trans. Image Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.neucom.2016.07.068","article-title":"Memristive pulse coupled neural network with applications in medical image processing","volume":"227","author":"Zhu","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.neucom.2017.04.075","article-title":"Artificial neural networks used in optimization problems","volume":"272","author":"Villarrubia","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/j.cam.2018.10.025","article-title":"A novel neural network for solving semidefinite programming problems with some applications","volume":"350","author":"Nikseresht","year":"2019","journal-title":"J. Comput. Appl. Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1426","DOI":"10.1016\/j.neucom.2017.09.078","article-title":"Combinatorial optimization of input features and learning parameters for decorrelated neural network ensemble-based soft measuring model","volume":"275","author":"Tang","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1109\/TNNLS.2016.2536104","article-title":"Co-operative coevolutionary neural networks for mining functional association rules","volume":"28","author":"Wang","year":"2017","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zhao, K.H., Zhao, X.X., and Lv, X.J. (2025). A general framework for the multiplicity of positive solutions to higher-order Caputo and Hadamard fractional functional differential coupled Laplacian systems. Fractal Fract., 9.","DOI":"10.3390\/fractalfract9110701"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1186\/s13662-025-04032-5","article-title":"A generalized stochastic Nicholson blowfly model with mixed time-varying lags and harvest control: Almost periodic oscillation and global stable behavior","volume":"2025","author":"Zhao","year":"2025","journal-title":"Adv. Contin. Discret. Model."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2127","DOI":"10.1007\/s11063-021-10722-4","article-title":"Existence and finite-time stability of Besicovitch almost periodic solutions of fractional-order quaternion-valued neural networks with time-varying delays","volume":"54","author":"Li","year":"2022","journal-title":"Neural Process. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.neunet.2016.05.003","article-title":"Synchronization of fractional-order complex-valued neural networks with time delay","volume":"81","author":"Bao","year":"2016","journal-title":"Neural Netw."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2423","DOI":"10.1109\/TNNLS.2016.2574842","article-title":"LMI conditions for global stability of fractional-order neural networks","volume":"28","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"105239","DOI":"10.1016\/j.cnsns.2020.105239","article-title":"Adaptive finite-time synchronization control for fractional-order complex-valued dynamical networks with multiple weights","volume":"85","author":"Xu","year":"2020","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.neucom.2016.02.002","article-title":"LMI conditions to global Mittag-Leffler stability of fractional-order neural networks with impulses","volume":"193","author":"Wu","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.matcom.2023.04.025","article-title":"Adaptive quasi-synchronization analysis for Caputo delayed Cohen\u2013Grossberg neural networks","volume":"212","author":"Zhang","year":"2023","journal-title":"Math. Comput. Simul."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.fss.2021.11.004","article-title":"Complete and finite-time synchronization of fractional-order fuzzy neural networks via nonlinear feedback control","volume":"443","author":"Li","year":"2022","journal-title":"Fuzzy Sets Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"7620","DOI":"10.1016\/j.jfranklin.2022.07.036","article-title":"New finite-time stability for fractional-order time-varying time-delay linear systems: A Lyapunov approach","volume":"359","author":"Gokul","year":"2022","journal-title":"J. Frankl. Inst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/j.matcom.2018.06.010","article-title":"Input-to-state stability of nonlinear impulsive systems via Lyapunov method involving indefinite derivative","volume":"155","author":"Li","year":"2019","journal-title":"Math. Comput. Simul."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"112311","DOI":"10.1016\/j.chaos.2022.112311","article-title":"Event-triggered hybrid impulsive control on lag synchronization of delayed memristor-based bidirectional associative memory neural networks for image hiding","volume":"161","author":"Yuan","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5321","DOI":"10.1109\/TNNLS.2021.3070136","article-title":"Uniform stability of Complex-valued neural networks of fractional order with linear impulses and fixed time delays","volume":"33","author":"Li","year":"2022","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_20","first-page":"102","article-title":"Stability of complex-valued impulsive system with delay","volume":"240","author":"Fang","year":"2014","journal-title":"Appl. Math. Comput."},{"key":"ref_21","first-page":"416","article-title":"Mittag-Leffler stability analysis of nonlinear fractional-order systems with impulses","volume":"293","author":"Yang","year":"2017","journal-title":"Appl. Math. Comput."},{"key":"ref_22","unstructured":"Podlubny, I. (1999). Fractional Differential Equations. Mathematics in Science and Engineering, Academic Press."},{"key":"ref_23","unstructured":"Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier Science B.V."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Haase, M. (2006). The functional calculus for sectorial operators. Operator Theory: Advances and Applications, Birkhauser.","DOI":"10.1007\/3-7643-7698-8"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3692","DOI":"10.1016\/j.na.2007.10.004","article-title":"Almost automorphic mild solutions to fractional differential equations","volume":"69","author":"Araya","year":"2009","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"ref_26","first-page":"793023","article-title":"Existence of the mild solutions for impulsive fractional equations with infinite delay","volume":"20","author":"Dabas","year":"2011","journal-title":"Int. J. Differ. Equ."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/15\/1\/17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T05:15:59Z","timestamp":1766985359000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/15\/1\/17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,26]]},"references-count":26,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["axioms15010017"],"URL":"https:\/\/doi.org\/10.3390\/axioms15010017","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,26]]}}}