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 (https://doi.org/10.1007/s10700-024-09422-0), 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.