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Partial derivatives of uncertain fields and uncertain partial differential equations

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  • Tingqing Ye

    (Beihang 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 defines partial derivatives of uncertain fields for the first time by putting forward the concept of Liu field. Then the fundamental theorem, chain rule and integration by parts of multivariate uncertain calculus are derived. Finally, this paper presents an uncertain partial differential equation, and gives its integral form.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:fuzodm:v:23:y:2024:i:2:d:10.1007_s10700-023-09417-3
    DOI: 10.1007/s10700-023-09417-3
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Tingqing Ye & Xiangfeng Yang, 2022. "Three-dimensional uncertain heat equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-19, January.
    4. Liu, Z. & Yang, Y., 2021. "Uncertain pharmacokinetic model based on uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    5. 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.
    6. Liu, Z. & Yang, Y., 2021. "Pharmacokinetic model based on multifactor uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    7. Tang, Han & Yang, Xiangfeng, 2021. "Uncertain chemical reaction equation," Applied Mathematics and Computation, Elsevier, vol. 411(C).
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    Cited by:

    1. Lu Yang & Yang Liu, 2025. "Numerical solution of uncertain partial differential equations and its applications," Fuzzy Optimization and Decision Making, Springer, vol. 24(1), pages 69-98, March.
    2. 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.

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