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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. Azizollah Babakhani & Dumitru Baleanu & Ravi P. Agarwal, 2013. "The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, March.
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    4. 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).
    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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