Fractional stochastic Volterra equation perturbed by fractional Brownian motion

In this paper, we consider a class of fractional stochastic Volterra equation of convolution type driven by infinite dimensional fractional Brownian motion with Hurst index h is an element of (0, 1). Base on the explicit formula for the scalar resolvent function and the properties of the Mittag-Leffler's function, the existence and regularity results of the stochastic convolution process are established. Separate proofs are required for the cases of Hurst parameter above and below 1/2 and it will turn out that the regularity of the solution increases with Hurst parameter h. (C) 2015 Elsevier Inc. All rights reserved.