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In order to describe the evolution of complex uncertain phenomenon related to belief degrees, we apply the complex Liu process to CUDEs. Firstly, we pose a concept of a linear CUDE and prove that homogeneous linear CUDE and general linear CUDE have solutions. Then, we prove existence and uniqueness theorem of a special CUDE. Further, we design a numerical algorithm to obtain inverse uncertainty distribution of the solution. Finally, as an application, we analyse the inverse uncertainty distributions of time integral of CUDEs and design numerical algorithms to obtain inverse uncertainty distributions of time integral.<\/jats:p>","DOI":"10.3233\/jifs-211030","type":"journal-article","created":{"date-parts":[[2021,7,16]],"date-time":"2021-07-16T10:19:16Z","timestamp":1626430756000},"page":"2275-2289","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Complex uncertain differential equations with application to time integral"],"prefix":"10.1177","volume":"41","author":[{"given":"Zhifu","family":"Jia","sequence":"first","affiliation":[{"name":"Nanjing University of Aeronautics and Astronautics","place":["China"]}]},{"given":"Xinsheng","family":"Liu","sequence":"additional","affiliation":[{"name":"Nanjing University of Aeronautics and Astronautics","place":["China"]}]}],"member":"179","published-online":{"date-parts":[[2021,7,11]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2019.08.006"},{"issue":"12","key":"e_1_3_2_3_2","first-page":"1","article-title":"Multi-wavelets galerkinmethod for solving the system of volterra integral equations","volume":"8","author":"Long H.","year":"2020","unstructured":"LongH., JebreenH. and TomasielloS., Multi-wavelets galerkinmethod for solving the system of volterra integral equations, Mathematics 8(12) (2020), 1\u201314.","journal-title":"Mathematics"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00034-019-01248-1"},{"issue":"6","key":"e_1_3_2_5_2","first-page":"1","article-title":"Fractional calculus of linerrelated fuzzy-valued functions related to Fr\u00e9chet differentiability","volume":"10","author":"Son N.","year":"2020","unstructured":"SonN., ThaoH., DongN., et al., Fractional calculus of linerrelated fuzzy-valued functions related to Fr\u00e9chet differentiability, Fuzzy Sets and Systems 10(6) (2020), 1\u201332.","journal-title":"Fuzzy Sets and Systems"},{"issue":"2","key":"e_1_3_2_6_2","first-page":"31","article-title":"On Goursat problem for fuzzy randompartial differential equations under generalized Lipschitzconditions","volume":"18","author":"Son N.","year":"2021","unstructured":"SonN., LongH. and DongN., On Goursat problem for fuzzy randompartial differential equations under generalized Lipschitzconditions, Iranian Journal of Fuzzy Systems 18(2) (2021), 31\u201349.","journal-title":"Iranian Journal of Fuzzy Systems"},{"issue":"2020","key":"e_1_3_2_7_2","first-page":"1","article-title":"Completecontrollability for a class of fractional evolution equations withuncertainty","volume":"104","author":"Son N.","unstructured":"SonN., DongN., SonL., KhastanA. and LongH., Completecontrollability for a class of fractional evolution equations withuncertainty, Evolution Equations & Control Theory 104(2020), 1\u201330.","journal-title":"Evolution Equations & Control Theory"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2020.105312"},{"issue":"16","key":"e_1_3_2_9_2","first-page":"1","article-title":"A New Continuous-Discrete FuzzyModel and Its Application in Finance","volume":"10","author":"Long H.","year":"2020","unstructured":"LongH., JebreenH. and CanoY., A New Continuous-Discrete FuzzyModel and Its Application in Finance, Mathematics 10(16) (2020), 1\u201315.","journal-title":"Mathematics"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym12101698"},{"key":"e_1_3_2_11_2","unstructured":"LiuB. 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