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On Caputo-Hadamard uncertain fractional differential equations

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  • Liu, Yiyu
  • Zhu, Yuanguo
  • Lu, Ziqiang

Abstract

The tool of uncertain fractional differential equations (UFDEs) is devoted to describing the behavior of complex systems with memory effects in the uncertain environment. In this paper, we mainly investigate the Caputo-Hadamard UFDEs. First, the definition of Caputo-Hadamard UFDE is proposed and the analytical solution to a linear Caputo-Hadamard UFDE is provided. Then, an existence and uniqueness theorem of solution to Caputo-Hadamard UFDE is studied.

Suggested Citation

  • Liu, Yiyu & Zhu, Yuanguo & Lu, Ziqiang, 2021. "On Caputo-Hadamard uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002472
    DOI: 10.1016/j.chaos.2021.110894
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    References listed on IDEAS

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    1. Huang, Lan-Lan & Baleanu, Dumitru & Mo, Zhi-Wen & Wu, Guo-Cheng, 2018. "Fractional discrete-time diffusion equation with uncertainty: Applications of fuzzy discrete fractional calculus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 166-175.
    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.
    3. 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.
    4. Baleanu, Dumitru & Wu, Guo–Cheng & Zeng, Sheng–Da, 2017. "Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 99-105.
    5. 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.
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