Ulam–Hyers Stability of Pantograph Hadamard Functional Fractional Stochastic Differential Equations

ABSTRACT In this article, we investigate a specific class of pantograph Hadamard functional fractional stochastic differential equations (FSDEs), which incorporate both proportional time delays and fractional derivatives. By leveraging Schauder's fixed point theorem and the contraction mapping principle, we establish the existence and uniqueness of solutions to the proposed system. Additionally, we explore the Ulam–Hyers stability (U‐H stability) of the system by applying the generalized Gr nwall inequality. To highlight the theoretical results, we provide some illustrative examples that demonstrates the practical implications of the established findings.