Asymptotic Behavior of Neutral Stochastic Partial Functional Integro-Differential Equations Driven by a Fractional Brownian Motion

This paper deals with the existence, uniqueness and asymptotic behavior of mild solutions to neutral stochastic delay functional integrodifferential equations perturbed by a fractional Brownian motion BH, with Hurst parameter (H \in ( \frac{1}{2} , 1)). The main tools for the existence of solution is a fixed point theorem and the theory of resolvent operators developed in Grimmer [R. Grimmer, Trans. Amer. Math. Soc., 273 (1982), 333349.], while a Gronwalltype lemma plays the key role for the asymptotic behavior. An example is provided to illustrate the results of this work.