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Solvability of a State–Dependence Functional Integro-Differential Inclusion with Delay Nonlocal Condition

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  • Taher S. Hassan

    (Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy)

  • Reda Gamal Ahmed

    (Faculty of Science, Al-Azhar University, Cairo 11884, Egypt)

  • Ahmed M. A. El-Sayed

    (Faculty of Science, Alexandria University, Alexandria 21522, Egypt)

  • Rami Ahmad El-Nabulsi

    (Research Center for Quantum Technology, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Mathematics and Physics Divisions, Athens Institute for Education and Research, 8 Valaoritou Street, Kolonaki, 10671 Athens, Greece)

  • Osama Moaaz

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia)

  • Mouataz Billah Mesmouli

    (Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

There is great focus on phenomena that depend on their past history or their past state. The mathematical models of these phenomena can be described by differential equations of a self-referred type. This paper is devoted to studying the solvability of a state-dependent integro-differential inclusion. The existence and uniqueness of solutions to a state-dependent functional integro-differential inclusion with delay nonlocal condition is studied. We, moreover, conclude the existence of solutions to the problem with the integral condition and the infinite-point boundary one. Some properties of the solutions are given. Finally, two examples illustrating the main result are presented.

Suggested Citation

  • Taher S. Hassan & Reda Gamal Ahmed & Ahmed M. A. El-Sayed & Rami Ahmad El-Nabulsi & Osama Moaaz & Mouataz Billah Mesmouli, 2022. "Solvability of a State–Dependence Functional Integro-Differential Inclusion with Delay Nonlocal Condition," Mathematics, MDPI, vol. 10(14), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2420-:d:860234
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    References listed on IDEAS

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    1. El-Sayed, A.M.A. & Ahmed, Reda Gamal, 2020. "Solvability of a coupled system of functional integro-differential equations with infinite point and Riemann–Stieltjes integral conditions," Applied Mathematics and Computation, Elsevier, vol. 370(C).
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