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Ulam-Hyers stability of caputo type fuzzy fractional differential equations with time-delays

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  • Wang, Xue
  • Luo, Danfeng
  • Zhu, Quanxin

Abstract

This paper is concerned with the Ulam-Hyers stability (UHs) of Caputo type fuzzy fractional differential equations (FFDEs) with time-delays. By applying Schauder’s fixed point theorem and a hypothetical condition, we explore the existence of the solutions. In addition, by using Banach contraction principle, we show the uniqueness of the solution of the system. What is more, we consider the UHs with aid of generalized Gro¨nwall inequality. Finally, an example with numerical simulation is provided to visualize the theoretical results.

Suggested Citation

  • Wang, Xue & Luo, Danfeng & Zhu, Quanxin, 2022. "Ulam-Hyers stability of caputo type fuzzy fractional differential equations with time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:chsofr:v:156:y:2022:i:c:s0960077922000339
    DOI: 10.1016/j.chaos.2022.111822
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    References listed on IDEAS

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    1. Qien Li & Danfeng Luo & Zhiguo Luo & Quanxin Zhu, 2019. "On the Novel Finite-Time Stability Results for Uncertain Fractional Delay Differential Equations Involving Noninstantaneous Impulses," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-9, September.
    2. Liu, Kui & Wang, JinRong & Zhou, Yong & O’Regan, Donal, 2020. "Hyers–Ulam stability and existence of solutions for fractional differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Aadhithiyan, S. & Raja, R. & Zhu, Q. & Alzabut, J. & Niezabitowski, M. & Lim, C.P., 2021. "Modified projective synchronization of distributive fractional order complex dynamic networks with model uncertainty via adaptive control," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
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    Cited by:

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    2. Daniela Marian & Sorina Anamaria Ciplea & Nicolaie Lungu, 2022. "Hyers–Ulam–Rassias Stability of Hermite’s Differential Equation," Mathematics, MDPI, vol. 10(6), pages 1-7, March.
    3. Chenkuan Li & Reza Saadati & Rekha Srivastava & Joshua Beaudin, 2022. "On the Boundary Value Problem of Nonlinear Fractional Integro-Differential Equations," Mathematics, MDPI, vol. 10(12), pages 1-14, June.
    4. Daniela Marian & Sorina Anamaria Ciplea & Nicolaie Lungu, 2022. "Hyers–Ulam Stability of Order k for Euler Equation and Euler–Poisson Equation in the Calculus of Variations," Mathematics, MDPI, vol. 10(15), pages 1-9, July.
    5. Huang, Jizhao & Luo, Danfeng & Zhu, Quanxin, 2023. "Relatively exact controllability for fractional stochastic delay differential equations of order κ∈(1,2]," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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