Stability in p -th moment for uncertain spring vibration equation

Abstract

Uncertain Differential equations are a type of differential equations driven by the Liu processes rather than the Wiener processes. Depending on the order of differentials it contains, an uncertain differential equation could be classified into first-order uncertain differential equation, second-order uncertain differential equation, third-order uncertain differential equation, and so on. The concepts of stability in various senses for the uncertain differential equations could be specified and applied to the uncertain spring vibration differential equations. However, to the best knowledge of mine, many types of stability have been proposed for first-order uncertain differential equations, for example, stability in mean, stability in p-th moment, stability in distribution, almost sure stability and exponential stability. However, stability in measure and stability in mean of high-order uncertain differential equations have been proposed. But only the concept of stability in mean and the concept of stability in measure have been proposed for high-order uncertain differential equations. In this paper, following the concept of stability in p-th moment for first-order uncertain differential equations, we present the concept of stability in p-th moment for general uncertain spring vibration differential equations which are a type of second-order uncertain differential equations.