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

TL;DR

This paper investigates second-order uncertain differential equations, introducing the concept of alpha-paths and deriving the inverse uncertainty distribution of their solutions, advancing understanding of higher-order UDEs.

Contribution

It proposes a pivotal monotonicity condition, introduces alpha-paths, and derives the inverse uncertainty distribution for solutions of higher-order UDEs.

Findings

Defined alpha-paths for UDEs

Established properties of alpha-paths

Derived inverse uncertainty distribution

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.