Polynomial Drift in Fractional Stochastic Differential Equations

We introduce a polynomial tensor-valued fractional stochastic operator and establish local wellposedness of the associated Volterra equation under local Lipschitz conditions. We establish properties for the FSDE forms that fit within our model by generating operators for drift and diffusion terms, and incorporating a tensor-based structure. Unlike standard FSDEs, our tensor framework explicitly captures higher-dimensional coupling and multilinear interactions required for complex physical systems. We prove that the associated Volterra operator is a contraction on a suitable Banach space, which we use to prove the existence, uniqueness, and interval of solutions for the model