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Stability Analysis Of Nonlinear Uncertain Fractional Differential Equations With Caputo Derivative

Author

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  • ZIQIANG LU

    (School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, P. R. China)

  • YUANGUO ZHU

    (School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, P. R. China)

  • QINYUN LU

    (School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, P. R. China)

Abstract

Uncertain fractional differential equation driven by Liu process plays a significant role in depicting the memory effects of uncertain dynamical systems. This paper mainly investigates the stability problems for the Caputo type of uncertain fractional differential equations with the order 0 < p ≤ 1. The concept of stability in measure of solutions to uncertain fractional differential equation is proposed based on uncertainty theory. Several sufficient conditions for ensuring the stability of the solutions are derived, respectively, in which the systems are divided into two cases with order 1 2 < p ≤ 1 and 0 < p ≤ 1 2. Some illustrative examples are performed to display the effectiveness of the proposed results.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:03:n:s0218348x21500572
    DOI: 10.1142/S0218348X21500572
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    Citations

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    Cited by:

    1. Lu, Ziqiang & Zhu, Yuanguo, 2022. "Nonlinear impulsive problems for uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Savin Treanţă & Tareq Saeed, 2022. "Duality Results for a Class of Constrained Robust Nonlinear Optimization Problems," Mathematics, MDPI, vol. 11(1), pages 1-17, December.
    3. Lu, Ziqiang & Zhu, Yuanguo, 2023. "Asymptotic stability in pth moment of uncertain dynamical systems with time-delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 323-335.

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