  Recently, the research community has been exploring fractional calculus to
address problems related to cosmology; in this approach, the gravitational
action integral is altered, leading to a modified Friedmann equation, then the
resulting theory is compared against observational data. In this context,
dynamical systems can be used along with an analysis the phase spaces for
different values of the fractional order of the derivative and their different
matter contents. The equilibrium points are classified, providing a range for
the order of the fractional derivative in order to investigate whether the
cosmological history can be reconstructed and a late-time accelerating
power-law solution obtained for the scale factor. In this paper, we discuss the
physical interpretation of the corresponding cosmological solutions with
particular emphasis on the influence of the fractional order of the derivative
in a theory of gravity that includes a scalar field minimally coupled to
gravity. The presented results improve and extend those obtained previously,
further demonstrating that fractional calculus can play a relevant role in
cosmology.
