  Mittag-Leffler analysis is an infinite dimensional analysis with respect to
non-Gaussian measures of Mittag-Leffler type which generalizes the powerful
theory of Gaussian analysis and in particular white noise analysis. In this
paper we further develop the Mittag-Leffler analysis by characterizing the
convergent sequences in the distribution space. Moreover we provide an
approximation of Donsker's delta by square integrable functions. Then we apply
the structures and techniques from Mittag-Leffler analysis in order to show
that a Green's function to the time-fractional heat equation can be constructed
using generalized grey Brownian motion (ggBm) by extending the fractional
Feynman-Kac formula from Schneider. Moreover we analyse ggBm, show its
differentiability in a distributional sense and the existence of corresponding
local times.
