Exact Solutions and Cosmological Constraints in Fractional Cosmology

This paper investigates exact solutions of cosmological interest in fractional cosmology. Given $\mu$, the order Caputo's derivative, and $w$, matter equation state, we present specific power-law solutions. We discuss general solution Riccati Equation, where for scale factor is a combination power laws. Using data, estimate free parameters. An analysis type Ia supernovae (SNe Ia) data observational Hubble parameter (OHD), also known as cosmic chronometers, joint with from SNe + OHD leads to best-fit values parameters calculated at $1\sigma$, $2\sigma$ $3\sigma$ confidence levels (CLs). On other hand, these are used calculate age Universe, current deceleration (both CL) density $1\sigma$ CL. Finding Universe roughly twice old one $\Lambda$CDM distinction Focusing our on results, can conclude that region which $\mu>2$ not ruled out by observations. relevant because cosmology gives without matter, accelerated $\mu>2$. origin model an state appealing $\Lambda$ or dark energy.