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On the De Blasi Measure of Noncompactness and Solvability of a Delay Quadratic Functional Integro-Differential Equation

Author

Listed:
  • Ahmed M. A. El-Sayed

    (Faculty of Science, Alexandria University, Alexandria 21521, Egypt)

  • Eman M. A. Hamdallah

    (Faculty of Science, Alexandria University, Alexandria 21521, Egypt)

  • Malak M. S. Ba-Ali

    (Faculty of Science, Princess Nourah Bint Abdul Rahman University, Riyadh 11671, Saudi Arabia)

Abstract

Quadratic integro-differential equations have been discussed in many works, for instance. Some analytic results on the existence and the uniqueness of problem solutions to quadratic integro-differential equations have been investigated in different classes. Various techniques have been applied such as measure of noncompactness, Schauder’s fixed point theorem and Banach contraction mapping. Here, we shall investigate quadratic functional integro-differential equations with delay. To prove the existence of solutions of the quadratic integro-differential equations, we use the technique of De Blasi measure of noncompactness. Moreover, we study some uniqueness results and continuous dependence of the solution on the initial condition and on the delay function. Some examples are presented to verify our results.

Suggested Citation

  • Ahmed M. A. El-Sayed & Eman M. A. Hamdallah & Malak M. S. Ba-Ali, 2022. "On the De Blasi Measure of Noncompactness and Solvability of a Delay Quadratic Functional Integro-Differential Equation," Mathematics, MDPI, vol. 10(9), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1362-:d:796981
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    References listed on IDEAS

    as
    1. M. Basseem & Ahmad Alalyani, 2020. "On the Solution of Quadratic Nonlinear Integral Equation with Different Singular Kernels," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-7, November.
    2. Józef Banaś & Szymon Dudek, 2013. "The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-15, April.
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