{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:38:54Z","timestamp":1777703934288,"version":"3.51.4"},"reference-count":20,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2017,7,7]],"date-time":"2017-07-07T00:00:00Z","timestamp":1499385600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2017,7,21]]},"abstract":"<jats:p>\n                    Uncertain variable and uncertain process are often employed to describe uncertainty phenomena. Uncertain variable is a measurable function from an uncertainty space to the real number set and uncertain process is essentially a sequence of uncertain variables indexed by time. Uncertain differential equation is a type of differential equation involving uncertain processes. Stability of uncertain differential equation plays a very important role in differential equation which means insensitivity of the state of a system to small changes in the initial state. In this paper, we focus on\n                    <jats:italic>p<\/jats:italic>\n                    th moment exponential stability of uncertain differential equation which is regarded as an extension of\n                    <jats:italic>p<\/jats:italic>\n                    th moment stability and exponential stability. Some stability theorems are given for uncertain differential equation, in which a sufficient and necessary condition for a linear uncertain differential equation being\n                    <jats:italic>p<\/jats:italic>\n                    th moment exponentially stable is provided.\n                  <\/jats:p>","DOI":"10.3233\/jifs-161836","type":"journal-article","created":{"date-parts":[[2017,7,7]],"date-time":"2017-07-07T11:47:55Z","timestamp":1499428075000},"page":"725-732","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["The\n                    <i>p<\/i>\n                    th moment exponential stability of uncertain differential equation"],"prefix":"10.1177","volume":"33","author":[{"given":"Xiumei","family":"Chen","sequence":"first","affiliation":[{"name":"School of Information Engineering, Shandong Youth University of Political Science, Jinan, China"},{"name":"Key Laboratory of Information Security and Intelligent Control in Universities of Shandong, Jinan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yufu","family":"Ning","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Shandong Youth University of Political Science, Jinan, China"},{"name":"Key Laboratory of Information Security and Intelligent Control in Universities of Shandong, Jinan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2017,7,7]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-012-0927-0"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-010-9073-2"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.7232\/iems.2013.12.1.002"},{"key":"e_1_3_2_5_2","first-page":"1","article-title":"On stochastic differential equations","volume":"4","author":"It\u00f4 K.","year":"1951","unstructured":"It\u00f4K., On stochastic differential equations, Memoirs of the American Mathematical Society 4 (1951), 1\u201351.","journal-title":"Memoirs of the American Mathematical Society"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.11.043"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73165-8_5"},{"issue":"1","key":"e_1_3_2_8_2","first-page":"3","article-title":"Fuzzy process, hybrid process and uncertain process","volume":"2","author":"Liu B.","year":"2008","unstructured":"LiuB., Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems 2(1) (2008), 3\u201316.","journal-title":"Journal of Uncertain Systems"},{"issue":"1","key":"e_1_3_2_9_2","first-page":"3","article-title":"Some research problems in uncertainty theory","volume":"3","author":"Liu B.","year":"2009","unstructured":"LiuB., Some research problems in uncertainty theory, Journal of Uncertain Systems 3(1) (2009), 3\u201310.","journal-title":"Journal of Uncertain Systems"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-13959-8"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1186\/2195-5468-1-1"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-014-9188-y"},{"issue":"4","key":"e_1_3_2_13_2","first-page":"244","article-title":"An analytic method for solving uncertain differential equations","volume":"6","author":"Liu Y.","year":"2012","unstructured":"LiuY., An analytic method for solving uncertain differential equations, Journal of Uncertain Systems 6(4) (2012), 244\u2013249.","journal-title":"Journal of Uncertain Systems"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-130812"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-015-1727-0"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.09.009"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-012-9139-4"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-120688"},{"key":"e_1_3_2_19_2","article-title":"A type of uncertain differential equations with analytic solution","volume":"1","author":"Yao K.","year":"2013","unstructured":"YaoK., A type of uncertain differential equations with analytic solution, Journal of Uncertainty Analysis and Applications 1 (2013), Article 8.","journal-title":"Journal of Uncertainty Analysis and Applications"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-014-9204-2"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1080\/01969722.2010.511552"}],"container-title":["Journal of Intelligent &amp; 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