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Parameter estimation for uncertain fractional differential equations

Author

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  • Liu He

    (Nanjing University of Science and Technology)

  • Yuanguo Zhu

    (Nanjing University of Science and Technology)

  • Ziqiang Lu

    (Nanjing Audit University)

Abstract

Since the concept of uncertain fractional differential equations was proposed, its wide range of applications have urged us to consider parameter estimation for uncertain fractional differential equations. In this paper, based on the definition of Liu process, we construct a function of unknown parameters which follows a standard normal uncertainty distribution. Then the method of moments is used to build a system of equations whose solutions are the estimated values of unknown parameters. After that, an algorithm of parameter estimation for a special uncertain fractional differential equation is proposed. Finally, the algorithm is applied to two numerical examples and the acceptability of the estimated parameters is proved by using uncertain hypothesis test.

Suggested Citation

  • Liu He & Yuanguo Zhu & Ziqiang Lu, 2023. "Parameter estimation for uncertain fractional differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(1), pages 103-122, March.
    • Handle: RePEc:spr:fuzodm:v:22:y:2023:i:1:d:10.1007_s10700-022-09385-0
    DOI: 10.1007/s10700-022-09385-0
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    References listed on IDEAS

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    Cited by:

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    2. Weiwei Wang & Dan A. Ralescu & Panpan Zhang, 2024. "Valuation of convertible bond based on uncertain fractional differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 23(4), pages 513-538, December.

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