New stability theorems of uncertain differential equations with time-dependent delay

Zhifu Jia; Xinsheng Liu; Zhifu Jia; Xinsheng Liu

doi:10.3934/math.2021038

AIMS Mathematics

2021, Volume 6, Issue 1: 623-642. doi: 10.3934/math.2021038

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Research article

New stability theorems of uncertain differential equations with time-dependent delay

Zhifu Jia ,
Xinsheng Liu ^,

State Key Laboratory of Mechanics and Control of Mechanical Structures, Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received: 08 August 2020 Accepted: 19 October 2020 Published: 23 October 2020
MSC : 65M12, 34K20

Stability in measure and stability in mean for uncertain differential equations with time-dependent delay have been investigated, which are not applicable for all situations, for the sake of completeness, this paper mainly gives the concepts of stability almost surely, in p-th moment and in distribution, and proves the sufficient conditions for uncertain differential equations with time-dependent delay being stable almost surely, in p-th moment and in distribution, respectively. In addition, the relationships among stability in measure, stability in p-th moment, and stability in distribution for the uncertain differential equation with time-dependent delay are also discussed.
- uncertain differential equations with time-dependent delay,
- stability almost surely,
- stability in p-th moment,
- stability in distribution
Citation: Zhifu Jia, Xinsheng Liu. New stability theorems of uncertain differential equations with time-dependent delay[J]. AIMS Mathematics, 2021, 6(1): 623-642. doi: 10.3934/math.2021038

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Abstract

Stability in measure and stability in mean for uncertain differential equations with time-dependent delay have been investigated, which are not applicable for all situations, for the sake of completeness, this paper mainly gives the concepts of stability almost surely, in p-th moment and in distribution, and proves the sufficient conditions for uncertain differential equations with time-dependent delay being stable almost surely, in p-th moment and in distribution, respectively. In addition, the relationships among stability in measure, stability in p-th moment, and stability in distribution for the uncertain differential equation with time-dependent delay are also discussed.

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