On Some Stochastic Parabolic Systems Driven by New Fractional Brownian Motions

Vector-valued functions of new fractional Brownian motions are considered. The concept of stochastic integrals are generalized. Formulas of Ito are also generalized. Some stochastic parabolic systems driven by new fractional Brownian motions are studied. Uniqueness and existence theorems are proved. These findings have potential applications in fields such as financial mathematics, where modeling with fractional Brownian motion is relevant.