  We present a new Aumann-like integral for a H\"older multifunction with
respect to a H\"older signal, based on the Young integral of a particular set
of H\"older selections. This restricted Aumann integral has continuity
properties that allow for numerical approximation as well as an existence
theorem for an abstract stochastic differential inclusion. This is applied to
concrete examples of first order and second order stochastic differential
inclusions directed by fractional Brownian motion.
