IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v161y2022ics0960077922005276.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922005276
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112317?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. H. Çerdik Yaslan, 2021. "Numerical solution of the nonlinear conformable space–time fractional partial differential equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 407-419, June.
    2. Darvishi, M.T. & Najafi, Mohammad & Wazwaz, Abdul-Majid, 2021. "Conformable space-time fractional nonlinear (1+1)-dimensional Schrödinger-type models and their traveling wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Ren, Jing & Zhai, Chengbo, 2020. "Stability analysis for generalized fractional differential systems and applications," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Aydin, Mustafa & Mahmudov, Nazim I., 2022. "On a study for the neutral Caputo fractional multi-delayed differential equations with noncommutative coefficient matrices," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    5. Usman Riaz & Akbar Zada & Zeeshan Ali & Ioan-Lucian Popa & Shahram Rezapour & Sina Etemad, 2021. "On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions," Mathematics, MDPI, vol. 9(11), pages 1-22, May.
    6. Shuyi Wang & Fanwei Meng, 2021. "Ulam Stability of n -th Order Delay Integro-Differential Equations," Mathematics, MDPI, vol. 9(23), pages 1-17, November.
    7. Osman Tunç, 2024. "New Results on the Ulam–Hyers–Mittag–Leffler Stability of Caputo Fractional-Order Delay Differential Equations," Mathematics, MDPI, vol. 12(9), pages 1-15, April.
    8. Selvam, Anjapuli Panneer & Govindaraj, Venkatesan, 2024. "Investigation of controllability and stability of fractional dynamical systems with delay in control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 89-104.
    9. Ma, Wangrong & Jin, Maozhu & Liu, Yifeng & Xu, Xiaobo, 2019. "Empirical analysis of fractional differential equations model for relationship between enterprise management and financial performance," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 17-23.
    10. 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).
    11. Chaudhary, Manish & Kumar, Rohit & Singh, Mritunjay Kumar, 2020. "Fractional convection-dispersion equation with conformable derivative approach," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    12. Ahmadova, Arzu & Mahmudov, Nazim I., 2021. "Ulam–Hyers stability of Caputo type fractional stochastic neutral differential equations," Statistics & Probability Letters, Elsevier, vol. 168(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005276. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.