IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i6p1044-d376742.html
   My bibliography  Save this article

Existence Results for Sequential Riemann–Liouville and Caputo Fractional Differential Inclusions with Generalized Fractional Integral Conditions

Author

Listed:
  • Jessada Tariboon

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

  • Sotiris K. Ntouyas

    (Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
    Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    These authors contributed equally to this work.)

  • Bashir Ahmad

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    These authors contributed equally to this work.)

  • Ahmed Alsaedi

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    These authors contributed equally to this work.)

Abstract

Under different criteria, we prove the existence of solutions for sequential fractional differential inclusions containing Riemann–Liouville and Caputo type derivatives and supplemented with generalized fractional integral boundary conditions. Our existence results rely on the endpoint theory, the Krasnosel’skiĭ’s fixed point theorem for multivalued maps and Wegrzyk’s fixed point theorem for generalized contractions. We demonstrate the application of the obtained results with the help of examples.

Suggested Citation

  • Jessada Tariboon & Sotiris K. Ntouyas & Bashir Ahmad & Ahmed Alsaedi, 2020. "Existence Results for Sequential Riemann–Liouville and Caputo Fractional Differential Inclusions with Generalized Fractional Integral Conditions," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1044-:d:376742
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/6/1044/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/6/1044/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Michał Kisielewicz, 2013. "Stochastic Differential Inclusions," Springer Optimization and Its Applications, in: Stochastic Differential Inclusions and Applications, edition 127, chapter 0, pages 147-179, Springer.
    2. Michał Kisielewicz, 2013. "Stochastic Differential Inclusions and Applications," Springer Optimization and Its Applications, Springer, edition 127, number 978-1-4614-6756-4, June.
    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. Miguel de Carvalho & Gabriel Martos, 2022. "Modeling interval trendlines: Symbolic singular spectrum analysis for interval time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(1), pages 167-180, January.
    2. Ahmed, Hamdy M. & Zhu, Quanxin, 2023. "Exploration nonlocal controllability for Hilfer fractional differential inclusions with Clarke subdifferential and nonlinear noise," Statistics & Probability Letters, Elsevier, vol. 195(C).
    3. Beatrice Acciaio & Anastasis Kratsios & Gudmund Pammer, 2022. "Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer," Papers 2201.13094, arXiv.org, revised Mar 2023.
    4. Bashir Ahmad & Ahmed Alsaedi & Sotiris K. Ntouyas & Hamed H. Al-Sulami, 2019. "On Neutral Functional Differential Inclusions involving Hadamard Fractional Derivatives," Mathematics, MDPI, vol. 7(11), pages 1-13, November.
    5. Ahmed Alsaedi & Ravi P. Agarwal & Sotiris K. Ntouyas & Bashir Ahmad, 2020. "Fractional-Order Integro-Differential Multivalued Problems with Fixed and Nonlocal Anti-Periodic Boundary Conditions," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    6. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Nisar, Kottakkaran Sooppy & Shukla, Anurag, 2021. "A note on the approximate controllability of Sobolev type fractional stochastic integro-differential delay inclusions with order 1," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1003-1026.
    7. Sotiris K. Ntouyas & Bashir Ahmad & Jessada Tariboon, 2022. "( k , ψ )-Hilfer Nonlocal Integro-Multi-Point Boundary Value Problems for Fractional Differential Equations and Inclusions," Mathematics, MDPI, vol. 10(15), pages 1-20, July.
    8. Zachary Feinstein & Birgit Rudloff, 2015. "A Supermartingale Relation for Multivariate Risk Measures," Papers 1510.05561, arXiv.org, revised Jan 2018.
    9. Mariusz Michta & Jerzy Motyl, 2022. "Set-Valued Functions of Bounded Generalized Variation and Set-Valued Young Integrals," Journal of Theoretical Probability, Springer, vol. 35(1), pages 528-549, March.
    10. Çağın Ararat & Zachary Feinstein, 2021. "Set-valued risk measures as backward stochastic difference inclusions and equations," Finance and Stochastics, Springer, vol. 25(1), pages 43-76, January.
    11. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy, 2021. "A note on approximate controllability for nonlocal fractional evolution stochastic integrodifferential inclusions of order r∈(1,2) with delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    12. Weixuan Xia, 2023. "Set-valued stochastic integrals for convoluted L\'{e}vy processes," Papers 2312.01730, arXiv.org, revised Aug 2024.

    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:8:y:2020:i:6:p:1044-:d:376742. 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.