SIGNIFICANT FINDINGS CONCERNING A SPECIFIC CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH FRACTIONAL-ORDER

Many real-world systems exhibit memory effects, where the current state depends not only on past states but also on delayed responses. Neutral stochastic fractional differential equations, which incorporate neutral terms to represent these delayed responses, offer a more accurate modeling framework than traditional stochastic differential equations. In this study, we establish significant results, including the existence and uniqueness of solutions for stochastic differential equations with neutral terms within the framework of Caputo–Hadamard fractional derivatives. Additionally, we derive results for the critical concept of the averaging principle. These findings are established in the [Formula: see text]th moment, generalizing the case for [Formula: see text]. Using contraction mapping techniques, we first prove the existence and uniqueness of solutions for a specific class of fractional-order stochastic differential equations. Next, we validate the averaging principle through inequality and interval translation methods. Finally, illustrative examples are provided to clarify and support the theoretical results.