  In this brief review, we present the results of the fractional differential
approach in cosmology in the context of the exact models of cosmological
accelerated expansion obtained by several authors to date. Most of these
studies are devoted to the problem of introducing fractional derivatives or
fractional integrals into the classical General Relativity (GR). There are
several observational and theoretical motivations to investigate the modified
or alternative theories of GR. Among other things, we cover General Relativity
modified by a phenomenological approach dealing with fractional calculus. At
the same time, a sufficiently large number of exact solutions of the
cosmological equations modified by this approach were obtained. Some of these
models may be especially relevant in the light of solving the problem of late
accelerated expansion of the universe. These studies are largely motivated by
rapid progress in the field of observational cosmology that now allows, for the
first time, precision tests of fundamental physics on the scale of the
observable Universe. The purpose of this review is to provide a reference tool
for researchers and students in cosmology and gravitational physics, as well as
a self-contained, comprehensive, and up-to-date introduction to the subject as
a whole.
