  Recently, a new field of study called fractional cosmology has emerged. It
uses fractional calculus to modify the standard derivative equations and change
the Friedmann equations. The evolution of cosmic species densities is also
affected by the $\mu$ fractional parameter and the age of the Universe $t_0$.
This new approach to cosmology modifies the Friedmann equations and allows for
a late cosmic acceleration without the need for a dark energy component. This
could be a breakthrough in solving longstanding problems in cosmology. By
analyzing observational Hubble data and Type Ia supernovae, we have been able
to place strict constraints on the fractional and cosmological parameters. Our
results suggest that the Universe may be older than previously estimated. We
also explore whether fractional cosmology can help resolve the $H_0$ tension.
