Abstract

The generalization of the Chamseddine–Connes spectral triples action to its (left and right) fractional counterpart is constructed within the context of the Riemann–Liouville and Erdelyi–Kober (left and right) fractional operators. In the fractional approach, the Dirac operators [Formula: see text] is approximated by [Formula: see text] and the spectral triple [Formula: see text] is replaced by its fractional equivalent [Formula: see text], [Formula: see text], [Formula: see text], 0 < α < 1. When the (left) fractional action is applied to the noncommutative space defined by the spectrum of the Standard Model, one obtains many attractive characteristics including time-dependent gauge couplings constants ([Formula: see text]), a time-dependent cosmological constant (Λ cos ), a time-dependent scalar Ricci curvature (R), a time-dependent Newton's coupling constant, and a time-dependent Higgs square mass [Formula: see text]. Furthermore, [Formula: see text], Λ cos , R, and [Formula: see text] were found to be nonsingulars at the Planck's time. When the (left and right) fractional bosonic action is taken into account, all the previous functions are found to be complexified, including gravity. Many additional interesting features are discussed and explored in some details.

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