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Nonparametric estimation for uncertain fractional differential equations

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  • He, Liu
  • Zhu, Yuanguo

Abstract

After uncertainty theory was established, it has become a new branch of mathematics and been applied to describing the indeterministic phenomena as an uncertain dynamic system. As an important part of uncertainty theory, uncertain fractional differential equation is a good tool to model some complex dynamic systems with uncertainties. Due to the lack of corresponding information, models of parametric uncertain fractional differential equation are not always available. Therefore, the requirement for nonparametric estimation of uncertain fractional differential equation is urgent. Utilizing the thought of Legendre polynomial approximation, we propose a method to estimate the nonparametric uncertain fractional differential equations. Then, the error analysis of this method is given. After that, the numerical simulation is applied to illustrating the validity of error analysis and show the errors between the approximating functions and actual functions. The stability of this method has also been verified without highly dense observations. Finally, by means of uncertain hypothesis test and Kolmogorov–Smirnov test, we prove the superiority of uncertain fractional differential equations for some examples.

Suggested Citation

  • He, Liu & Zhu, Yuanguo, 2024. "Nonparametric estimation for uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:chsofr:v:178:y:2024:i:c:s0960077923012444
    DOI: 10.1016/j.chaos.2023.114342
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    References listed on IDEAS

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    1. Lifen Jia & Wei Chen, 2021. "Uncertain SEIAR model for COVID-19 cases in China," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 243-259, June.
    2. Liu, Z., 2021. "Generalized moment estimation for uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    3. Liu, Zhe & Yang, Ying, 2022. "Moment estimation for parameters in high-order uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    4. Jin, Ting & Sun, Yun & Zhu, Yuanguo, 2020. "Time integral about solution of an uncertain fractional order differential equation and application to zero-coupon bond model," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    5. 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).
    6. Jin, Ting & Zhu, Yuanguo, 2020. "First hitting time about solution for an uncertain fractional differential equation and application to an uncertain risk index model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    7. 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.
    8. 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.
    9. Tingqing Ye & Baoding Liu, 2022. "Uncertain hypothesis test with application to uncertain regression analysis," Fuzzy Optimization and Decision Making, Springer, vol. 21(2), pages 157-174, June.
    10. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    11. Guanzhong Ma & Xiangfeng Yang & Xiao Yao, 2021. "A relation between moments of Liu process and Bernoulli numbers," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 261-272, June.
    12. Agrawal, Khushbu & Kumar, Ranbir & Kumar, Sunil & Hadid, Samir & Momani, Shaher, 2022. "Bernoulli wavelet method for non-linear fractional Glucose–Insulin regulatory dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    13. Xiaowei Chen & Jing Li & Chen Xiao & Peilin Yang, 2021. "Numerical solution and parameter estimation for uncertain SIR model with application to COVID-19," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 189-208, June.
    14. Lu, Ziqiang & Zhu, Yuanguo & Li, Bo, 2019. "Critical value-based Asian option pricing model for uncertain financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 694-703.
    15. Altan, Aytaç & Karasu, Seçkin & Bekiros, Stelios, 2019. "Digital currency forecasting with chaotic meta-heuristic bio-inspired signal processing techniques," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 325-336.
    16. Waichon Lio & Baoding Liu, 2021. "Initial value estimation of uncertain differential equations and zero-day of COVID-19 spread in China," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 177-188, June.
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