On the Ulam stability of fuzzy differential equations

Zhenyu Jin; Jianrong Wu; Zhenyu Jin; Jianrong Wu

doi:10.3934/math.2020384

AIMS Mathematics

2020, Volume 5, Issue 6: 6006-6019. doi: 10.3934/math.2020384

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Research article

On the Ulam stability of fuzzy differential equations

Zhenyu Jin ,
Jianrong Wu ^,

College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, Jiangsu 215009, P. R. China

Received: 10 April 2020 Accepted: 20 July 2020 Published: 23 July 2020
MSC : 03E72, 34D99, 34G99

Ulam stability problems have received considerable attention in the field of differential equations. However, how to effectively build the fuzzy model for Ulam stability problems is less attractive due to varies of differentiabilities requirements. The paper discusses the Ulam stability of fuzzy differential equations in Banach spaces. After introducing the new definitions of differentiabilities for fuzzy number-valued mappings, we give some important properties about these differentiabilities. On these bases, with different differentiabilities and conditions, we prove the Ulam stability of three kinds of fuzzy differential equations. The obtained conclusions generalize the existing results.
- fuzzy sets,
- differential equations,
- Ulam stability,
- Banach spaces
Citation: Zhenyu Jin, Jianrong Wu. On the Ulam stability of fuzzy differential equations[J]. AIMS Mathematics, 2020, 5(6): 6006-6019. doi: 10.3934/math.2020384

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Abstract

Ulam stability problems have received considerable attention in the field of differential equations. However, how to effectively build the fuzzy model for Ulam stability problems is less attractive due to varies of differentiabilities requirements. The paper discusses the Ulam stability of fuzzy differential equations in Banach spaces. After introducing the new definitions of differentiabilities for fuzzy number-valued mappings, we give some important properties about these differentiabilities. On these bases, with different differentiabilities and conditions, we prove the Ulam stability of three kinds of fuzzy differential equations. The obtained conclusions generalize the existing results.

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