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Finite-time stability of uncertain fractional difference equations

Author

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  • Qinyun Lu

    (Nanjing University of Science and Technology)

  • Yuanguo Zhu

    (Nanjing University of Science and Technology)

Abstract

Uncertain fractional difference equations may preferably describe the behavior of the systems with the memory effect and discrete feature in the uncertain environment. So it is of great significance to investigate their stability. In this paper, the concept of finite-time stability almost surely for uncertain fractional difference equations is introduced. A finite-time stability theorem is then stated by Mittag–Leffler function and proved by a generalized Gronwall inequality on a finite time. Some examples are finally presented to illustrate the validity of our results.

Suggested Citation

  • Qinyun Lu & Yuanguo Zhu, 2020. "Finite-time stability of uncertain fractional difference equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(2), pages 239-249, June.
    • Handle: RePEc:spr:fuzodm:v:19:y:2020:i:2:d:10.1007_s10700-020-09318-9
    DOI: 10.1007/s10700-020-09318-9
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    References listed on IDEAS

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    1. Lu, Ziqiang & Zhu, Yuanguo, 2019. "Numerical approach for solution to an uncertain fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 137-148.
    2. Ziqiang Lu & Hongyan Yan & Yuanguo Zhu, 2019. "European option pricing model based on uncertain fractional differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 18(2), pages 199-217, June.
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    Cited by:

    1. Jian Zhou & Yujiao Jiang & Athanasios A. Pantelous & Weiwen Dai, 2023. "A systematic review of uncertainty theory with the use of scientometrical method," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 463-518, September.
    2. Zhiyong Huang & Chunliu Zhu & Jinwu Gao, 2021. "Stability analysis for uncertain differential equation by Lyapunov’s second method," Fuzzy Optimization and Decision Making, Springer, vol. 20(1), pages 129-144, March.

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