We employ Riesz’s fractional derivative into the Wheeler-DeWitt (WDW) equation for a closed de Sitter geometry and obtain the no-boundary and tunneling wave functions. From the corresponding probability distributions, the event horizon of the nucleated universe can be a fractal surface with dimensions between $2\le D<3$. Concretely, the tunneling wave function 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 toward (nontrivial compact) flat and open scenarios. Our 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.

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• Inflation
• Quantum cosmology
• Quantum gravity