Existence, Uniqueness, and Averaging Principle for a Class of Fractional Neutral Itô–Doob Stochastic Differential Equations

ABSTRACT This paper explores the existence, uniqueness, and averaging principles of neutral fractional stochastic Itô–Doob differential equations (NFSIDDEs). By utilizing the Picard iteration technique (PIT), we establish the existence and uniqueness of solutions. Additionally, we demonstrate the averaging principle for NFSIDDEs through the utilization of key inequalities, including the Gronwall and Hölder inequalities. Our findings contribute to a deeper understanding of the qualitative behavior and stability properties of NFSIDDEs, incorporating the fields of neutral fractional calculus, stochastic analysis, and classical inequalities.