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Global Existence for an Implicit Hybrid Differential Equation of Arbitrary Orders with a Delay

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 paper, we present a qualitative study of an implicit fractional differential equation involving Riemann–Liouville fractional derivative with delay and its corresponding integral equation. Under some sufficient conditions, we establish the global and local existence results for that problem by applying some fixed point theorems. In addition, we have investigated the continuous and integrable solutions for that problem. Moreover, we discuss the continuous dependence of the solution on the delay function and on some data. Finally, further results and particular cases are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:967-:d:773597
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    References listed on IDEAS

    as
    1. Juan J. Nieto & Abelghani Ouahab & Venktesh Venktesh, 2015. "Implicit Fractional Differential Equations via the Liouville–Caputo Derivative," Mathematics, MDPI, vol. 3(2), pages 1-14, May.
    2. Ahmed M. A. El-Sayed & Hind H. G. Hashem & Shorouk M. Al-Issa, 2021. "An Implicit Hybrid Delay Functional Integral Equation: Existence of Integrable Solutions and Continuous Dependence," Mathematics, MDPI, vol. 9(24), pages 1-14, December.
    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.
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