Existence of solutions and exponential -moment estimates for non-linear G-SFDEs

This article develops novel Formula: see text-moment exponential stability criteria for stochastic functional differential equations driven by G-Brownian motion. Assuming a semi-monotone condition, the uniqueness of the solutions has been ensured. The core of our contribution is a set of new lemmas designed to advance research in this field. We analyze the boundedness of the Yosida approximations and use it to prove the existence of solutions. Our analysis demonstrates the Formula: see text-moment exponential stability. The theoretical results are illustrated with an example.