Abstract
The semi-classical regime of fractional quantum cosmology has been discussed based on the Wheeler-DeWitt equation and ADM-Hamiltonian formalism. Fractionality has been introduced through two different approaches: the first one is based on fractional Dunkl Laplacian operator and the second one based on fractal calculus. Our models generalize the recent approaches of fractional quantum cosmology introduced in literature. In the first approach, it was revealed that power-law inflation and large number of e-folds may be obtained for various values of the fractional parameter. However, the second approach is plausible only if the cosmological constant decays with the scale factor of the universe. We have confronted our model with observations based on the Bayesian hierarchical model that describes the full distance ladder from nearby geometric anchors through Cepheids to Hubble-Flow SNe we have estimated the numerical values of the fractional order parameter. In both scenarios, the number of e-folds is too large.Pacs numbers: 05.45.Df, 45.10.Hj, 98.80.-k
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