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Nonlinear impulsive problems for uncertain fractional differential equations

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  • Lu, Ziqiang
  • Zhu, Yuanguo

Abstract

This paper deals with the impulsive problem for uncertain fractional dynamical system. Firstly, the concept of uncertain fractional impulsive problem involving the Caputo derivative is introduced and the analytic solutions to several linear uncertain fractional impulsive problems are derived with the help of the Mittag-Leffler functions. Then the existence and uniqueness theorems are developed via the Kuratowski measure of noncompactness and fixed point theorems, respectively. Finally, an illustrative example is provided to explain our main results.

Suggested Citation

  • Lu, Ziqiang & Zhu, Yuanguo, 2022. "Nonlinear impulsive problems for uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001680
    DOI: 10.1016/j.chaos.2022.111958
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    References listed on IDEAS

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    1. Yang, Xiangfeng & Ralescu, Dan A., 2015. "Adams method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 993-1003.
    2. 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.
    3. Pshtiwan Othman Mohammed & Thabet Abdeljawad & Fahd Jarad & Yu-Ming Chu, 2020. "Existence and Uniqueness of Uncertain Fractional Backward Difference Equations of Riemann–Liouville Type," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-8, October.
    4. 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.
    5. Anh, P.T. & Doan, T.S. & Huong, P.T., 2019. "A variation of constant formula for Caputo fractional stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 351-358.
    6. Ziqiang Lu & Yuanguo Zhu & Qinyun Lu, 2021. "Stability Analysis Of Nonlinear Uncertain Fractional Differential Equations With Caputo Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-10, May.
    7. Hu, Lunhu & Kang, Rui & Pan, Xing & Zuo, Dujun, 2020. "Risk assessment of uncertain random system—Level-1 and level-2 joint propagation of uncertainty and probability in fault tree analysis," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
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