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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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)

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