Cosmological Models with Fractional Derivatives and Fractional Action Functional

TL;DR

This paper develops cosmological models incorporating fractional derivatives and fractional action principles, providing exact solutions to these novel equations to explore alternative gravitational theories.

Contribution

It introduces and analyzes cosmological models based on fractional calculus, deriving exact solutions that extend traditional Einstein-Hilbert action frameworks.

Findings

Exact solutions for fractional cosmological equations are obtained.

Fractional derivatives lead to new dynamical behaviors in cosmology.

The models offer alternative explanations for cosmic evolution.

Abstract

Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional order, are constructed. A number of exact solutions to those equations of fractional cosmological models in both cases is given.