Existence and uniqueness theoremfor uncertain spring vibration equation

Article type: Research Article

Authors: Jia, Lifen^a | Yang, Xiangfeng^{b; *}

Affiliations: [a] Department of Mathematical Sciences, Tsinghua University, Beijing, China | [b] School of Information Technology and Management, University of International Business and Economics, Beijing, China

Correspondence: [*] Corresponding author. Xiangfeng Yang, School of Information Technology and Management, University of International Business and Economics, Beijing 100029, China. Tel: +86 1064495031; E-mail: [email protected].

Abstract: Uncertain spring vibration equation is a type of uncertain differential equations, whose external force is affected by an uncertain interference. The solution and inverse uncertainty distribution of solution of uncertain spring vibration equation in different cases have been derived, respectively. This paper proves an existence and uniqueness theorem of solution for general uncertain spring vibration equation in different cases under linear growth condition and Lipschitz condition.

Keywords: Spring vibration equation, uncertain differential equation, uncertain process, uncertainty theory

DOI: 10.3233/JIFS-18467

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 2, pp. 2607-2617, 2018