  This paper is devoted to study a class of stochastic Volterra equations
associated with fractional Brownian motion. We first prove the Driver type
integration by parts formula and the shift Harnack type inequalities. As a
direct application, we provide an alternative method to describe the
regularities of the law of the solution. Secondly, by using the Malliavin
calculus, the Bismut type derivative formula is established, which is then
applied to the study of the gradient estimate and the strong Feller property.
Finally, we establish the Talagrand type transportation cost inequalities for
the law of the solution on the path space with respect to both the uniform
metric and the $L^2$-metric.
