Extensive exploration of multi-term hybrid functional equation vıa hybrid differential feedback control

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.