Existence and Attractivity Results for First-Order Random Differential Equations via Fixed Point Theorems

Abstract

In this paper, we investigate the existence and attractivity of solutions to a class of first-order random differential equations by using the well-known Random Banach Fixed Point Theorem. The stochastic nature of the system is modeled via measurable random operators and integrability conditions. Using Carathéodory-type assumptions and compactness arguments, we establish sufficient conditions under which a unique random solution exists. A lemma is provided to convert the random differential equation into an equivalent random integral equation. Furthermore, we construct a verified example satisfying all conditions of the main theorem. This study contributes to the growing body of literature on stochastic analysis and fixed point theory in random metric spaces.