Complex uncertain differential equations with application to time integral

Article type: Research Article

Authors: Jia, Zhifu | Liu, Xinsheng^{; *}

Affiliations: State Key Laboratory of Mechanics and Control of Mechanical Structures, Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China

Correspondence: [*] Corresponding author. Xinsheng Liu. E-mail: xsliu@nuaa.edu.cn.

Abstract: In this paper, we propose complex uncertain differential equations (CUDEs) based on uncertainty theory. 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.

Keywords: Complex uncertain differential equations, existence and uniqueness theorem, time integral

DOI: 10.3233/JIFS-211030

Journal: Journal of Intelligent & Fuzzy Systems, vol. 41, no. 1, pp. 2275-2289, 2021