Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion

In this paper Fokker-Planck-Kolmogorov type equations associated with stochastic differential equations driven by a time-changed fractional Brownian motion are derived. Two equivalent forms are suggested. The time-change process considered is the first hitting time process for either a stable subordinator or a mixture of stable subordinators. A family of operators arising in the representation of the Fokker-Plank-Kolmogorov equations is shown to have the semigroup property.