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

Taher S. Hassan, Reda Gamal Ahmed, Ahmed M. A. El-Sayed, Rami Ahmad El-Nabulsi, Osama Moaaz and Mouataz Billah Mesmouli
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Taher S. Hassan: Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia
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
Osama Moaaz: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Mouataz Billah Mesmouli: Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia

Mathematics, 2022, vol. 10, issue 14, 1-18

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.

Keywords: nonlocal condition; infinite point; delay integral operator; differential inclusion; self-dependence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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