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Research Article | Open Access

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

Zeman Wang1, Zhong Liu1, Zikun Han2, Xiuying Guo1, Qiubao Wang1,2( )
Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
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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 α-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 equationsinverse uncertainty distributionα-paths
CLC number: 47E05, 34A12

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AIMS Mathematics
Volume 9 Issue 11,
November 2024
Pages 33023-33061
DOI: 10.3934/math.20241579

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Cite this article:
Wang Z, Liu Z, Han Z, et al. The inverse uncertainty distribution of the solutions to a class of higher-order uncertain differential equations. AIMS Mathematics, 2024, 9(11): 33023-33061. https://doi.org/10.3934/math.20241579

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Received: 19 September 2024
Revised: 26 October 2024
Accepted: 06 November 2024
Published: 21 November 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)