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Higher-order partial derivatives of uncertain field with application to higher-order uncertain partial differential equation

Author

Listed:
  • Binhao He

    (Tsinghua University)

  • Baoding Liu

    (Tsinghua University)

Abstract

Multivariate uncertain calculus is a branch of mathematics that deals with differentiation and integration of uncertain fields based on uncertainty theory. This paper revises the definition of first partial derivatives of uncertain field and defines higher-order partial derivatives for the first time. Then some sufficient and necessary conditions for uncertain fields possessing partial derivatives are derived. Finally, some examples are documented to verify the solution of higher-order uncertain partial differential equation.

Suggested Citation

  • Binhao He & Baoding Liu, 2025. "Higher-order partial derivatives of uncertain field with application to higher-order uncertain partial differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 24(2), pages 317-342, June.
    • Handle: RePEc:spr:fuzodm:v:24:y:2025:i:2:d:10.1007_s10700-025-09448-y
    DOI: 10.1007/s10700-025-09448-y
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    References listed on IDEAS

    as
    1. Tingqing Ye & Baoding Liu, 2023. "Uncertain hypothesis test for uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 195-211, June.
    2. Yang Liu & Baoding Liu, 2022. "Residual analysis and parameter estimation of uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 513-530, December.
    3. Kaixi Zhang & Baoding Liu, 2024. "Higher-order derivative of uncertain process and higher-order uncertain differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 23(2), pages 295-318, June.
    4. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    5. Tingqing Ye, 2024. "Partial derivatives of uncertain fields and uncertain partial differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 23(2), pages 199-217, June.
    6. Zhe Liu & Yanbin Li, 2024. "Pricing and valuation of carbon swap in uncertain finance market," Fuzzy Optimization and Decision Making, Springer, vol. 23(3), pages 319-336, September.
    7. Xiangfeng Yang & Hua Ke, 2023. "Uncertain interest rate model for Shanghai interbank offered rate and pricing of American swaption," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 447-462, September.
    8. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    9. Xiangfeng Yang & Kai Yao, 2017. "Uncertain partial differential equation with application to heat conduction," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 379-403, September.
    10. Lu Yang & Yang Liu, 2024. "Solution method and parameter estimation of uncertain partial differential equation with application to China’s population," Fuzzy Optimization and Decision Making, Springer, vol. 23(1), pages 155-177, March.
    Full references (including those not matched with items on IDEAS)

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