Analysis of fractional stochastic systems driven by fractional Brownian motion with general memory kernel

Fractional stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm) have attracted growing attention due to their ability to model systems exhibiting non-Markovian dynamics and long-range dependence, which naturally arise in many real-world phenomena characterized by hereditary and persistent randomness. In this work, we establish the existence and uniqueness of mild solutions using the Picard iteration technique for the case where the Hurst parameter satisfies $H\in \left(\frac{1}{2},1\right)$. Moreover, we establish the approximate controllability of the systems under suitable conditions. To generalize the theoretical framework, we employ the Caputo–Katugampola fractional derivative (CKFD), thereby extending the analysis to a broader class of fractional stochastic systems.