EXTENSIVE EXPLORATION OF MULTI-TERM HYBRID FUNCTIONAL EQUATION VIA HYBRID DIFFERENTIAL FEEDBACK CONTROL

Year 2025, Volume: 15 Issue: 10, 2421 - 2438, 01.10.2025

Ahmed M.a. El-sayed , Sh. M Al-ıssa , H. H. G. Hashem I. H. Kaddoura A. A. Najdi

Abstract

This paper investigates the existence of solutions for a multidimensional hybrid functional equation with multiple delays, incorporating differential feedback control. The focus is on finding well-defined, continuous, and bounded solutions on the semi-infinite interval. To establish the existence of these solutions, we employ measures of noncompactness associated with a specified modulus of continuity within the space \( BC(\mathbb{R}_{+}) \). Furthermore, we derive sufficient conditions to ensure the asymptotic stability of the solutions to this integral equation. An illustrative example is provided to demonstrate the applicability of the theoretical results.

Keywords

multi-term hybrid functional equation , existence of continuous solution , a measure of noncompactness , Darbofixed-point theorem , differential feedback control

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