  We employ Riesz's fractional derivative into the Wheeler--DeWitt equation for
a closed de Sitter geometry and obtain the no-boundary and tunneling
wavefunctions. From the corresponding probability distributions, the event
horizon of the nucleated universe can be a fractal surface with dimensions
between $2\leq D<3$. Concretely, the tunneling wavefunction favors fractal
dimensions less than $2.5$ and an accelerated power-law phase. Differently, the
no-boundary proposal conveys fractal dimensions close to $3$, with the universe
instead entering a decelerated phase. Subsequently, we extend our discussion
towards (non-trivial compact) flat and open scenarios. Results suggest that
given the probability of creation of a closed inflationary universe in the
tunneling proposal is exponentially suppressed, a flat or an open universe
becomes favored within fractional inflationary quantum universe.
