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

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

A. M. A. El-Sayed , S. M. Al-Issa , H. H. G. Hashem, I. H. Kaddoura , A. A. Najdi

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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(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.