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doi: 10.3934/jimo.2021073
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## Uncertain spring vibration equation

 1 School of Management and Engineering, Capital University of Economics and Business, Beijing, China 2 Department of Financial Engineering, Central University of Finance and Economics, Beijing 100081, China

* Corresponding author: Wei Dai

Received  July 2020 Revised  January 2021 Early access April 2021

Fund Project: The first author is supported by the Beijing Municipal Education Commission Foundation of China (No. KM202110038001), the Young Academic Innovation Team of Capital University of Economics and Business (No. QNTD202002), and the special fund of basic scientific research business fees of Beijing Municipal University of Capital University of Economics and Business (No. XRZ2020016)

The spring vibration equation is to model the behavior of a spring which has a time varying force acting on it. The stochastic spring vibration equation was proposed for modeling spring vibration phenomena with noise described by Wiener process. However, there exists a paradox in some cases. Thus, as a counterpart, this paper proposes uncertain spring vibration equation driven by Liu process to describe the noise. Moreover, the analytic solution of uncertain spring vibration equation is derived and the inverse uncertainty distribution of solution is proved. At last, this paper presents a paradox of stochastic spring vibration equation.

Citation: Lifen Jia, Wei Dai. Uncertain spring vibration equation. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021073
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##### References:
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