  Considering the Friedmann--Lema\^{i}tre--Robertson--Walker (FLRW) metric and
the Einstein scalar field system as an underlying gravitational model to
construct fractional cosmological models has interesting implications in both
classical and quantum regimes. Regarding the former, we just review the most
fundamental approach to establishing an extended cosmological model. We
demonstrate that employing new methodologies allows us to obtain exact
solutions. Despite the corresponding standard models, we cannot use any
arbitrary scalar potentials; instead, it is determined from solving three
independent fractional field equations. This article concludes with an overview
of a fractional quantum/semi-classical model that provides an inflationary
scenario.
