Affiliations: State Key Laboratory of Mechanics and Control of Mechanical Structures, Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China
Correspondence:
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Corresponding author. Xinsheng Liu, State Key Laboratory of Mechanics and Control of Mechanical Structures, Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China. E-mail: xsliu@nuaa.edu.cn.
Abstract: Uncertain pantograph differential equation (UPDE for short) is a special unbounded uncertain delay differential equation. Stability in measure, stability almost surely and stability in p-th moment for uncertain pantograph differential equation have been investigated, which are not applicable for all situations, for the sake of completeness, this paper mainly gives the concept of stability in distribution, and proves the sufficient condition for uncertain pantograph differential equation being stable in distribution. In addition, the relationships among stability almost surely, stability in measure, stability in p-th moment, and stability in distribution for the uncertain pantograph differential equation are also discussed.
Keywords: uncertainty theory, uncertain pantograph differential equation, stability in distribution, the relationships among stabilities
