{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T07:00:25Z","timestamp":1769583625424,"version":"3.49.0"},"reference-count":25,"publisher":"SAGE Publications","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2024,2,14]]},"abstract":"<jats:p>As a complex uncertain differential equation, how to solve the multi-dimensional uncertain differential equation is a complicated and difficult problem. This paper will be devoted to the \u03b1-path of some special multi-dimensional uncertain differential equations, namely, multi-factor uncertain differential equations, nested uncertain differential equations and multi-factor nested uncertain differential equations. The \u03b1-path method is used to study the numerical solution problems of the above three special multi-dimensional uncertain differential equations. At the same time, the inverse uncertainty distributions and expected values of these three special multi-dimensional uncertain differential equations are also obtained. At last, the numerical algorithm examples are given to verify it.<\/jats:p>","DOI":"10.3233\/jifs-234432","type":"journal-article","created":{"date-parts":[[2024,1,5]],"date-time":"2024-01-05T10:43:44Z","timestamp":1704451424000},"page":"4761-4776","source":"Crossref","is-referenced-by-count":0,"title":["The \u03b1-path of multi-dimensional uncertain differential equations and its applications"],"prefix":"10.1177","volume":"46","author":[{"given":"Xiaoli","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Xinjiang University, Urumqi, China"}]},{"given":"Chongguo","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Xinjiang University, Urumqi, China"}]},{"given":"Gang","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Xinjiang University, Urumqi, 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