Research article

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

  • 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.

    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

    Related Papers:

  • 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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