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An Implicit Hybrid Delay Functional Integral Equation: Existence of Integrable Solutions and Continuous Dependence

Author

Listed:
  • Ahmed M. A. El-Sayed

    (Faculty of Science, Alexandria University, Alexandria 21544, 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.)

  • Shorouk M. Al-Issa

    (Department of Mathematics, Faculty of Arts and Sciences, The International University of Beirut, Beirut 1107, Lebanon
    These authors contributed equally to this work.
    Current address: Department of Mathematics, Faculty of Arts and Sciences, Lebanese International University, Saida 1600, Lebanon.)

Abstract

In this work, we are discussing the solvability of an implicit hybrid delay nonlinear functional integral equation. We prove the existence of integrable solutions by using the well known technique of measure of noncompactnes. Next, we give the sufficient conditions of the uniqueness of the solution and continuous dependence of the solution on the delay function and on some functions. Finally, we present some examples to illustrate our results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3234-:d:702099
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    Cited by:

    1. 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.
    2. Ahmed M. A. El-Sayed & Malak M. S. Ba-Ali & Eman M. A. Hamdallah, 2023. "Asymptotic Stability and Dependency of a Class of Hybrid Functional Integral Equations," Mathematics, MDPI, vol. 11(18), pages 1-18, September.

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