{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T17:12:22Z","timestamp":1787677942416,"version":"build-2784847793"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2015,3,27]],"date-time":"2015-03-27T00:00:00Z","timestamp":1427414400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2016,4]]},"DOI":"10.1007\/s00521-015-1876-1","type":"journal-article","created":{"date-parts":[[2015,3,26]],"date-time":"2015-03-26T15:55:48Z","timestamp":1427385348000},"page":"549-556","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":104,"title":["Finite-time stability criteria for a class of fractional-order neural networks with delay"],"prefix":"10.1007","volume":"27","author":[{"given":"Liping","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cong","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ranchao","family":"Wu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yigang","family":"He","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Chai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2015,3,27]]},"reference":[{"key":"1876_CR1","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.neucom.2013.05.018","volume":"121","author":"R Rakkiyappan","year":"2013","unstructured":"Rakkiyappan R, Chandrasekar A, Lakshmanan S, Park J, Jung H (2013) Effects of leakage time-varying delays in Markovian jump neural networks with impulse control. Neurocomputing 121:365\u2013378","journal-title":"Neurocomputing"},{"key":"1876_CR2","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/j.neucom.2013.10.018","volume":"131","author":"R Rakkiyappan","year":"2014","unstructured":"Rakkiyappan R, Chandrasekar A, Lakshmanan S, Park J (2014) Exponential stability of Markovian jumping stochastic Cohen\u2013Grossberg neural networks with mode-dependent probabilistic time-varying delays and impulses. Neurocomputing 131:265\u2013277","journal-title":"Neurocomputing"},{"issue":"9","key":"1876_CR3","doi-asserted-by":"crossref","first-page":"1459","DOI":"10.1109\/TNNLS.2013.2256796","volume":"24","author":"T Li","year":"2013","unstructured":"Li T, Wang T, Song A, Fei S (2013) Combined convex technique on delay-dependent stability for delayed neural networks. IEEE Trans Neural Netw Learn Syst 24(9):1459\u20131466","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"7\u20138","key":"1876_CR4","doi-asserted-by":"crossref","first-page":"1707","DOI":"10.1007\/s00521-013-1383-1","volume":"24","author":"X Wang","year":"2014","unstructured":"Wang X, Li C, Huang T, Duan S (2014) Global exponential stability of a class of memristive neural networks with time-varying delays. Neural Comput Appl 24(7\u20138):1707\u20131715","journal-title":"Neural Comput Appl"},{"issue":"3","key":"1876_CR5","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.1016\/j.jfranklin.2013.11.017","volume":"351","author":"R Rakkiyappan","year":"2014","unstructured":"Rakkiyappan R, Zhu Q, Chandrasekar A (2014) Stability of stochastic neural networks of neutral type with markovian jumping parameters: A delay fractioning approach. J Franklin Inst 351(3):1553\u20131570","journal-title":"J Franklin Inst"},{"key":"1876_CR6","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.neunet.2013.03.016","volume":"44","author":"M Xiao","year":"2013","unstructured":"Xiao M, Zheng W, Cao J (2013) Bifurcation and control in a neural network with small and large delays. Neural Netw 44:132\u2013142","journal-title":"Neural Netw"},{"key":"1876_CR7","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1038\/nn.2212","volume":"11","author":"B Lundstrom","year":"2008","unstructured":"Lundstrom B, Higgs M, Spain W, Fairhall A (2008) Fractional differentiation by neocortical pyramidal neurons. Nat Neurosci 11:1335\u20131342","journal-title":"Nat Neurosci"},{"key":"1876_CR8","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/BF00206239","volume":"72","author":"T Anastasio","year":"1994","unstructured":"Anastasio T (1994) The fractional-order dynamics of brainstem vestibulooculomotor neurons. Biol Cybern 72:69\u201379","journal-title":"Biol Cybern"},{"issue":"6","key":"1876_CR9","doi-asserted-by":"crossref","first-page":"1655","DOI":"10.1016\/j.camwa.2012.01.019","volume":"64","author":"G Anastassiou","year":"2012","unstructured":"Anastassiou G (2012) Fractional neural network approximation. Comput Math Appl 64(6):1655\u20131676","journal-title":"Comput Math Appl"},{"key":"1876_CR10","doi-asserted-by":"crossref","unstructured":"Boroomand A, Menhaj M (2009) Fractional-order Hopfield neural networks. Lecture Notes in Computer Science 5506:883\u2013890","DOI":"10.1007\/978-3-642-02490-0_108"},{"key":"1876_CR11","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1103\/PhysRevE.61.776","volume":"61","author":"P Arena","year":"2000","unstructured":"Arena P, Fortua L, Porto D (2000) Chaotic behavior in noninteger-order cellular neural networks. Phys Rev E 61:776\u2013781","journal-title":"Phys Rev E"},{"issue":"3","key":"1876_CR12","doi-asserted-by":"crossref","first-page":"1350044","DOI":"10.1142\/S0218127413500442","volume":"23","author":"L Liu","year":"2013","unstructured":"Liu L, Liu C, Liang D (2013) Hyperchaotic behavior in arbitrary-dimensional fractional-order quantum cellular neural network model. Int J Bifurc Chaos 23(3):1350044","journal-title":"Int J Bifurc Chaos"},{"key":"1876_CR13","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.neunet.2012.02.030","volume":"32","author":"E Kaslik","year":"2012","unstructured":"Kaslik E, Sivasundaram S (2012) Nonlinear dynamics and chaos in fractional-order neural networks. Neural Netw 32:245\u2013256","journal-title":"Neural Netw"},{"key":"1876_CR14","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.neucom.2012.01.011","volume":"94","author":"X Huang","year":"2012","unstructured":"Huang X, Zhao Z, Wang Z, Li Y (2012) Chaos and hyperchaos in fractional-order cellular neural networks. Neurocomputing 94:13\u201321","journal-title":"Neurocomputing"},{"issue":"2","key":"1876_CR15","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1088\/0253-6102\/60\/2\/08","volume":"60","author":"R Wu","year":"2013","unstructured":"Wu R, Hei X, Chen L (2013) Finite-time stability of fractional-order neural networks with delay. Commun Theor Phys 60(2):189\u2013193","journal-title":"Commun Theor Phys"},{"key":"1876_CR16","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/j.neucom.2012.11.034","volume":"111","author":"L Chen","year":"2013","unstructured":"Chen L, Chai Y, Wu R, Ma T, Zhai H (2013) Dynamic analysis of a class of fractional-order neural networks with delay. Neurocomputing 111:190\u2013194","journal-title":"Neurocomputing"},{"key":"1876_CR17","doi-asserted-by":"crossref","unstructured":"Alofi A, Cao J, Elaiw A, Al-Mazrooei A (2014) Delay-dependent stability criterion of Caputo fractional neural networks with distributed delay. Discret Dyn Nat Soc, 529358","DOI":"10.1155\/2014\/529358"},{"issue":"8","key":"1876_CR18","doi-asserted-by":"crossref","first-page":"3265","DOI":"10.3390\/e15083355","volume":"15","author":"L Chen","year":"2013","unstructured":"Chen L, Qu J, Chai Y, Wu R, Qi G (2013) Synchronization of a class of fractional-order chaotic neural networks. Entropy 15(8):3265\u20133276","journal-title":"Entropy"},{"issue":"4","key":"1876_CR19","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1016\/j.chaos.2006.07.033","volume":"36","author":"S Zhou","year":"2008","unstructured":"Zhou S, Hua L, Zhua Z (2008) Chaos control and synchronization in a fractional neuron network system. Chaos Solitons Fractals 36(4):973\u2013984","journal-title":"Chaos Solitons Fractals"},{"key":"1876_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.neunet.2013.11.016","volume":"51","author":"J Chen","year":"2014","unstructured":"Chen J, Zeng Z, Jiang P (2014) Global Mittag\u2013Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Netw 51:1\u20138","journal-title":"Neural Netw"},{"key":"1876_CR21","unstructured":"Dorato P (1961) Short time stability in linear time-varying systems. In: Proceedings of IRE international convention record part 4:83\u201387"},{"key":"1876_CR22","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/j.amc.2007.07.069","volume":"197","author":"X Zhang","year":"2008","unstructured":"Zhang X (2008) Some results of linear fractional order time-delay system. Appl Math Comput 197:407\u2013411","journal-title":"Appl Math Comput"},{"issue":"3\u20134","key":"1876_CR23","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/j.mcm.2008.09.011","volume":"49","author":"M Lazarevic","year":"2009","unstructured":"Lazarevic M, Spasic A (2009) Finite-time stability analysis of fractional order time-delay systems: Gronwall\u2019s approach. Math Comput Model 49(3\u20134):475\u2013481","journal-title":"Math Comput Model"},{"issue":"4","key":"1876_CR24","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1111\/j.1934-6093.2005.tb00407.x","volume":"7","author":"M Lazarevic","year":"2005","unstructured":"Lazarevic M, Debeljkovic D (2005) Finite time stability analysis of linear autonomous fractional order systems with delayed state. Asian J Control 7(4):440\u2013447","journal-title":"Asian J Control"},{"issue":"2","key":"1876_CR25","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.mechrescom.2005.08.010","volume":"33","author":"M Lazarevic","year":"2006","unstructured":"Lazarevic M (2006) Finite time stability analysis of PD $$^\\alpha $$ \u03b1 fractional control of robotic time-delay systems. Mech Res Commun 33(2):269\u2013279","journal-title":"Mech Res Commun"},{"key":"1876_CR26","doi-asserted-by":"crossref","first-page":"2129C2140","DOI":"10.1007\/s11071-014-1594-8","volume":"78","author":"M Aghababa","year":"2014","unstructured":"Aghababa M (2014) A Lyapunov-based control scheme for robust stabilization of fractional chaotic systems. Nonlinear Dyn 78:2129C2140","journal-title":"Nonlinear Dyn"},{"key":"1876_CR27","author":"M Roohi","year":"2014","unstructured":"Roohi M, Aghababa M, Haghighi A (2014) Switching adaptive controllers to control fractional-order complex systems with unknown structure and input nonlinearities. Complexity. doi: 10.1002\/cplx.21598","journal-title":"Complexity"},{"key":"1876_CR28","doi-asserted-by":"crossref","unstructured":"Aghababa M (2014) Synchronization and stabilization of fractional second-order nonlinear complex systems. Nonlinear Dyn. doi: 10.1007\/s11071-014-1411-4","DOI":"10.1007\/s11071-014-1411-4"},{"key":"1876_CR29","author":"M Aghababa","year":"2014","unstructured":"Aghababa M (2014) Fractional modeling and control of a complex nonlinear energy supply-demand system. Complexity. doi: 10.1002\/cplx.21533","journal-title":"Complexity"},{"issue":"2","key":"1876_CR30","first-page":"133","volume":"6","author":"A Haghighi","year":"2014","unstructured":"Haghighi A, Aghababa M, Roohi M (2014) Robust stabilization of a class of three-dimensional uncertain fractional-order non-autonomous systems. Int J Ind Math 6(2):133\u2013139","journal-title":"Int J Ind Math"},{"issue":"3","key":"1876_CR31","doi-asserted-by":"crossref","first-page":"031003","DOI":"10.1115\/1.4025771","volume":"9","author":"M Aghababa","year":"2014","unstructured":"Aghababa M (2014) Control of fractional-order systems using chatter-free sliding mode approach. J Comput Nonlinear Dyn 9(3):031003","journal-title":"J Comput Nonlinear Dyn"},{"issue":"3","key":"1876_CR32","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1007\/s11071-013-1087-1","volume":"75","author":"M Aghababa","year":"2014","unstructured":"Aghababa M (2014) A switching fractional calculus-based controller for normal non-linear dynamical systems. Nonlinear Dyn 75(3):577\u2013588","journal-title":"Nonlinear Dyn"},{"issue":"3","key":"1876_CR33","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1177\/0142331213509399","volume":"36","author":"M Aghababa","year":"2014","unstructured":"Aghababa M (2014) Control of nonlinear non-integer-order systems using variable structure control theory. Trans Inst Measure Control 36(3):425\u2013432","journal-title":"Trans Inst Measure Control"},{"issue":"4","key":"1876_CR34","doi-asserted-by":"crossref","first-page":"2329","DOI":"10.1007\/s11071-013-0944-2","volume":"73","author":"M Aghababa","year":"2013","unstructured":"Aghababa M (2013) No-chatter variable structure control for fractional nonlinear complex systems. Nonlinear Dyn 73(4):2329\u20132342","journal-title":"Nonlinear Dyn"},{"key":"1876_CR35","doi-asserted-by":"crossref","first-page":"1744","DOI":"10.1080\/00207179.2013.796068","volume":"86","author":"M Aghababa","year":"2013","unstructured":"Aghababa M (2013) Design of a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems. Int J Control 86:1744\u20131756","journal-title":"Int J Control"},{"issue":"1\u20132","key":"1876_CR36","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1007\/s11071-013-0822-y","volume":"73","author":"M Aghababa","year":"2013","unstructured":"Aghababa M (2013) A novel terminal sliding mode controller for a class of non-autonomous fractional-order systems. Nonlinear Dyn 73(1\u20132):679\u2013688","journal-title":"Nonlinear Dyn"},{"issue":"1\u20132","key":"1876_CR37","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s11071-011-0261-6","volume":"69","author":"M Aghababa","year":"2012","unstructured":"Aghababa M (2012) Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique. Nonlinear Dyn 69(1\u20132):247\u2013261","journal-title":"Nonlinear Dyn"},{"key":"1876_CR38","doi-asserted-by":"crossref","first-page":"2670","DOI":"10.1016\/j.cnsns.2011.10.028","volume":"17","author":"M Aghababa","year":"2012","unstructured":"Aghababa M (2012) Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller. Commun Nonlinear Sci Numer Simul 17:2670\u20132681","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"1","key":"1876_CR39","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/S0898-1221(97)00096-5","volume":"187","author":"Y Chen","year":"2007","unstructured":"Chen Y, Ahn H, Podlubny I (2007) Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality. Appl Math Comput 187(1):27\u201334","journal-title":"Appl Math Comput"},{"issue":"4","key":"1876_CR40","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1016\/j.isatra.2009.04.006","volume":"48","author":"K Moornani","year":"2009","unstructured":"Moornani K, Mohammad H (2009) On robust stability of linear time invariant fractional-order systems with real parametric uncertainties. ISA Trans 48(4):484\u2013490","journal-title":"ISA Trans"},{"issue":"4","key":"1876_CR41","doi-asserted-by":"crossref","first-page":"1062","DOI":"10.1109\/TAC.2012.2218064","volume":"58","author":"Y Lim","year":"2013","unstructured":"Lim Y, Oh K, Ahn H (2013) Stability and stabilization of fractional-order linear systems subject to input saturation. IEEE Trans Autom Control 58(4):1062\u20131067","journal-title":"IEEE Trans Autom Control"},{"issue":"4","key":"1876_CR42","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s11071-006-9094-0","volume":"48","author":"W Deng","year":"2007","unstructured":"Deng W, Li C, Lu J (2007) Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn 48(4):409\u2013416","journal-title":"Nonlinear Dyn"},{"key":"1876_CR43","doi-asserted-by":"crossref","unstructured":"Sadati S, Baleanu D, Ranjbar A, Ghaderi R, Abdeljawad T (2010) Mittag\u2013Leffler stability theorem for fractional nonlinear systems with delay. Abstr Appl Anal, 108651","DOI":"10.1155\/2010\/108651"},{"issue":"2","key":"1876_CR44","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1016\/j.amc.2006.08.163","volume":"187","author":"C Li","year":"2007","unstructured":"Li C, Deng W (2007) Remarks on fractional derivatives. Appl Math Comput 187(2):777\u2013784","journal-title":"Appl Math Comput"},{"key":"1876_CR45","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-99970-3","volume-title":"Analytic inequalities","author":"D Mitrinovic","year":"1970","unstructured":"Mitrinovic D (1970) Analytic inequalities. Springer, Berlin"},{"key":"1876_CR46","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/BF00257405","volume":"15","author":"D Willett","year":"1964","unstructured":"Willett D (1964) Nonlinear vector integral equations as contraction mappings. Arch Ration Mech Anal 15:79\u201386","journal-title":"Arch Ration Mech Anal"},{"key":"1876_CR47","doi-asserted-by":"crossref","first-page":"5940","DOI":"10.1103\/PhysRevE.59.5940","volume":"59","author":"J Cao","year":"1999","unstructured":"Cao J (1999) Global stability analysis in delayed cellular neural networks. Phys Rev E 59:5940\u20135944","journal-title":"Phys Rev E"},{"key":"1876_CR48","author":"X Yang","year":"2014","unstructured":"Yang X, Song Q, Liu Y, Zhao Z (2014) Finite-time stability analysis of fractional-order neural networks with delay. Neurocomputing. doi: 10.1016\/j.neucom.2014.11.023i","journal-title":"Neurocomputing"},{"key":"1876_CR49","doi-asserted-by":"crossref","unstructured":"Ke Y, Miao C (2014) Stability analysis of fractional-order CohenCGrossberg neural networks with time delay. Int J Comput Math. doi: 10.1080\/00207160.2014.935734","DOI":"10.1080\/00207160.2014.935734"},{"key":"1876_CR50","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1016\/j.neucom.2014.07.060","volume":"149","author":"R Wu","year":"2015","unstructured":"Wu R, Lu Y, Chen L (2015) Finite-time stability of fractional delayed neural networks. Neurocomputing 149:700\u2013707","journal-title":"Neurocomputing"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-015-1876-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-015-1876-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-015-1876-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,8]],"date-time":"2024-06-08T01:30:15Z","timestamp":1717810215000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-015-1876-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,27]]},"references-count":50,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,4]]}},"alternative-id":["1876"],"URL":"https:\/\/doi.org\/10.1007\/s00521-015-1876-1","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,27]]}}}