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Existence results and Ulam type stability for conformable fractional oscillating system with pure delay

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  • Li, Mengmeng
  • Wang, JinRong

Abstract

In this paper, we firstly introduce a concept of conformable fractional delayed type matrix Cosine and Sine functions, which help us to construct an exact expression of a solution for the conformable fractional oscillating delay systems (CFODs). Secondly, we show existence and uniqueness of solutions of nonlinear conformable oscillating delay system with using a fixed point theorem. Finally, as an application, this paper is concerned with the Ulam-Hyers stability (UHs) and Ulam-Hyers-Rassias stability (UHRs) of CFODs on finite time interval.

Suggested Citation

  • Li, Mengmeng & Wang, JinRong, 2022. "Existence results and Ulam type stability for conformable fractional oscillating system with pure delay," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005276
    DOI: 10.1016/j.chaos.2022.112317
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    References listed on IDEAS

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    1. 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).
    2. Mahmudov, Nazim I. & Aydın, Mustafa, 2021. "Representation of solutions of nonhomogeneous conformable fractional delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Thabet, Hayman & Kendre, Subhash, 2018. "Analytical solutions for conformable space-time fractional partial differential equations via fractional differential transform," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 238-245.
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