IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i21p4068-d959911.html
   My bibliography  Save this article

Development on a Fractional Hybrid Differential Inclusion with a Nonlinear Nonlocal Fractional-Order Integral Inclusion

Author

Listed:
  • Ahmed M. A. El-Sayed

    (Faculty of Science, Alexandria University, Alexandria 21544, Egypt
    These authors contributed equally to this work.)

  • Sheren A. Abd El-Salam

    (Faculty of Sciences, Damanhour University, Damanhour 22511, Egypt
    These authors contributed equally to this work.)

  • Hind H. G. Hashem

    (Faculty of Science, Alexandria University, Alexandria 21544, Egypt
    These authors contributed equally to this work.)

Abstract

In this article, we consider a Riemann–Liouville fractional-order nonlinear hybrid delay differential inclusion with a nonlinear set-valued nonlocal integral condition of fractional order. We prove some existence and uniqueness results in C ( I , R ) . We also study the continuous dependence of the solutions on the two sets of selections of the two set-valued functions, considered in our problem, and on some other parameters. Finally, to validate our results, we present an example and some particular cases.

Suggested Citation

  • Ahmed M. A. El-Sayed & Sheren A. Abd El-Salam & Hind H. G. Hashem, 2022. "Development on a Fractional Hybrid Differential Inclusion with a Nonlinear Nonlocal Fractional-Order Integral Inclusion," Mathematics, MDPI, vol. 10(21), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4068-:d:959911
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/21/4068/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/21/4068/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. El-Sayed, A.M.A. & Gaafar, F.M., 2001. "Fractional-order differential equations with memory and fractional-order relaxation-oscillation model," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 12(3), pages 296-310.
    2. E. Ahmed & A. M. A. El-Sayed & A. E. M. El-Mesiry & H. A. A. El-Saka, 2005. "Numerical Solution For The Fractional Replicator Equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1017-1025.
    3. Zidane Baitiche & Kaddour Guerbati & Mouffak Benchohra & Yong Zhou, 2019. "Boundary Value Problems for Hybrid Caputo Fractional Differential Equations," Mathematics, MDPI, vol. 7(3), pages 1-11, March.
    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. Allaberen Ashyralyev & Sa’adu Bello Mu’azu, 2023. "Bounded Solutions of Semi-Linear Parabolic Differential Equations with Unbounded Delay Terms," Mathematics, MDPI, vol. 11(16), pages 1-14, August.
    2. Yingkang Xie & Zhen Wang & Bo Meng, 2019. "Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    3. Ahmed M. A. El-Sayed & Sheren A. Abd El-Salam & Hind H. G. Hashem, 2022. "Global Existence for an Implicit Hybrid Differential Equation of Arbitrary Orders with a Delay," Mathematics, MDPI, vol. 10(6), pages 1-13, March.
    4. Matouk, A.E. & Lahcene, Bachioua, 2023. "Chaotic dynamics in some fractional predator–prey models via a new Caputo operator based on the generalised Gamma function," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    5. Devi, Amita & Kumar, Anoop, 2022. "Hyers–Ulam stability and existence of solution for hybrid fractional differential equation with p-Laplacian operator," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    6. Rashid, Saima & Jarad, Fahd & Alsharidi, Abdulaziz Khalid, 2022. "Numerical investigation of fractional-order cholera epidemic model with transmission dynamics via fractal–fractional operator technique," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    7. Vidushi Gupta & Arshad Ali & Kamal Shah & Syed Abbas, 2021. "On stability analysis of hybrid fractional boundary value problem," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(1), pages 27-38, March.

    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:gam:jmathe:v:10:y:2022:i:21:p:4068-:d:959911. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.