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Recently, a new field of study called fractional cosmology has emerged. Ituses fractional calculus to modify the standard derivative equations and changethe Friedmann equations. The evolution of cosmic species densities is alsoaffected by the $\mu$ fractional parameter and the age of the Universe $t_0$.This new approach to cosmology modifies the Friedmann equations and allows fora late cosmic acceleration without the need for a dark energy component. Thiscould be a breakthrough in solving longstanding problems in cosmology. Byanalyzing observational Hubble data and Type Ia supernovae, we have been ableto place strict constraints on the fractional and cosmological parameters. Ourresults suggest that the Universe may be older than previously estimated. Wealso explore whether fractional cosmology can help resolve the $H_0$ tension.

Cosmology under the fractional calculus approach: a possible $H_0$ tension resolution?