The inverse uncertainty distribution of the solutions to a class of higher-order uncertain differential equations

Abstract

In this paper, we study the higher-order uncertain differential equations (UDEs) as defined by Kaixi Zhang [11], mainly focus on the second-order case. We propose a pivotal condition (monotonicity in some sense, see more details in Section 3), introduce the concept of $ \alpha $-paths of UDEs, and demonstrate its properties. Based on this, we derive the inverse uncertainty distribution of the solution. Finally, we present numerical examples to substantiate the rationality of the condition.

Keywords

• higher-order uncertain differential equations
• inverse uncertainty distribution
• $ \alpha $-paths