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Existence and uniqueness of solutions to uncertain fractional switched systems with an uncertain stock model

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  • Shu, Yadong
  • Li, Bo

Abstract

In this paper, an uncertain fractional switched system is a fractional switched system disturbed by subjective uncertainty, which can be written by Caputo type of uncertain fractional differential equations. Few results concerning uncertain fractional systems were published before. To fill this gap, the property of solutions to uncertain fractional switched systems with finite-time horizon is investigated in depth. Based on two conditions called linear growth condition and Lipschitz condition, an existence and uniqueness theorem of solutions is proposed for the uncertain fractional switched systems, and the strict demonstration is given for the theorem in terms of uncertainty theory and Banach fixed point theorem. Finally, an uncertain stock model is proposed and analyzed to illustrate the effectiveness of the results obtained.

Suggested Citation

  • Shu, Yadong & Li, Bo, 2022. "Existence and uniqueness of solutions to uncertain fractional switched systems with an uncertain stock model," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921011000
    DOI: 10.1016/j.chaos.2021.111746
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    References listed on IDEAS

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    1. He, Lingyun & Banihashemi, Seddigheh & Jafari, Hossein & Babaei, Afshin, 2021. "Numerical treatment of a fractional order system of nonlinear stochastic delay differential equations using a computational scheme," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
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    3. 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).
    4. Zhi-Wei Lv & Bao-Feng Chen, 2014. "Existence and Uniqueness of Positive Solutions for a Fractional Switched System," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, April.
    5. 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.
    6. Weiwei Wang & Dan A. Ralescu, 2021. "Option pricing formulas based on uncertain fractional differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 20(4), pages 471-495, December.
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    Cited by:

    1. Luo, Lingao & Li, Lulu & Huang, Wei, 2024. "Asymptotic stability of fractional-order Hopfield neural networks with event-triggered delayed impulses and switching effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 491-504.

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