Transform of Riccati equation of constant coefficients through fractional procedure

TL;DR

This paper introduces a fractional calculus approach to transform and solve Riccati equations with constant coefficients, applying it to cosmological models in barotropic FRW cosmologies.

Contribution

It presents a novel fractional generalization of Riccati equations and provides solutions applicable to cosmological equations recently studied by Faraoni.

Findings

Derived solutions for the fractional Riccati equation

Applied results to cosmological Riccati equations

Extended classical Riccati analysis using fractional calculus

Abstract

We use a particular fractional generalization of the ordinary differential equations that we apply to the Riccati equation of constant coefficients. By this means the latter is transformed into a modified Riccati equation with the free term expressed as a power of the independent variable which is of the same order as the order of the applied fractional derivative. We provide the solutions of the modified equation and employ the results for the case of the cosmological Riccati equation of FRW barotropic cosmologies that has been recently introduced by Faraoni