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On the oscillation of Caputo fractional differential equations with Mittag–Leffler nonsingular kernel

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  • Abdalla, Bahaaeldin
  • Abdeljawad, Thabet

Abstract

In this article, we derive sufficient conditions to prove the oscillation for solutions of Caputo fractional differential equations with Mittag–Leffler nonsingular kernel of the form{(aABCDκ0ξ)(t)+ϕ1(t,ξ)=θ(t)+ϕ2(t,ξ),t>aξk(a)=bk(k=0,1,…,n),where n<κ0≤n+1 and aABCDκ0 is the left-fractional Caputo derivative with Mittag–Leffler nonsingular kernel or the Atangana–Baleanu fractional derivative in the sense of Caputo. An example is given to validate part of the proven results.

Suggested Citation

  • Abdalla, Bahaaeldin & Abdeljawad, Thabet, 2019. "On the oscillation of Caputo fractional differential equations with Mittag–Leffler nonsingular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 173-177.
    • Handle: RePEc:eee:chsofr:v:127:y:2019:i:c:p:173-177
    DOI: 10.1016/j.chaos.2019.07.001
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    References listed on IDEAS

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    1. Abdeljawad, Thabet & Baleanu, Dumitru, 2017. "Monotonicity analysis of a nabla discrete fractional operator with discrete Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 106-110.
    2. Abdeljawad, Thabet, 2019. "Fractional difference operators with discrete generalized Mittag–Leffler kernels," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 315-324.
    3. Jarad, Fahd & Abdeljawad, Thabet & Hammouch, Zakia, 2018. "On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 16-20.
    4. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    5. Bin Zheng & Qinghua Feng, 2013. "Some New Oscillation Criteria for a Class of Nonlinear Fractional Differential Equations with Damping Term," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, November.
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    Cited by:

    1. Li, Xiaoyan, 2021. "Comment for “Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel”," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Omar Bazighifan & Thabet Abdeljawad, 2020. "Improved Approach for Studying Oscillatory Properties of Fourth-Order Advanced Differential Equations with p -Laplacian Like Operator," Mathematics, MDPI, vol. 8(5), pages 1-11, April.

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