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

Fractional-order derivatives in cosmological models of accelerated expansion