Analytical Solutions for a Nonlinear Quadratic Delayed Functional Integral Inclusion With Feedback Control on the Real Half-Line

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DOI: https://doi.org/10.28924/2291-8639-22-2024-178
Published: Oct 2, 2024
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Ahmed M. A. El-Sayed, Nesreen F. M. El-Haddad, Analytical Solutions for a Nonlinear Quadratic Delayed Functional Integral Inclusion With Feedback Control on the Real Half-Line, Int. J. Anal. Appl., 22 (2024), 178.

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Ahmed M. A. El-Sayed, Nesreen F. M. El-Haddad

Abstract

Let E be a reflexive Banach space. In this research, we are interested in the solvability of the nonlinear quadratic delayed functional integral inclusion (NQDFII) with a feedback control condition on the real half-axis. Our examination is found within the space BC(R+, E) of bounded continuous functions on the real half-axis R+ and takes values in a reflexive Banach space E beneath the assumption that the set-valued function G satisfy Lipschitz condition in E. The base we depend on in this study is the procedure related to a measure of noncompactness in the space BC(R+, E) by a given norm of continuity and applying Darbo’s fixed point theorem. Moreover, the asymptotic stability of the solution and the asymptotic dependency of the solution on the set of selections SG will be examined. Also, we give an example to illustrate the adequacy and esteem of our comes about.

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