  Holographic dark energy theories present a fascinating interface to probe
late-time cosmology, as guided by contemporary ideas about quantum gravity. In
this work, we present a new holographic dark energy scenario designated
Fractional Holographic Dark Energy (FHDE). This model extends the conventional
framework of HDEs by incorporating specific features from fractional calculus
recently applied, e.g., in cosmological settings. In this manner, we retrieve a
novel form of HDE energy density. We then show how FHDE can provide a
consistent picture of the evolution of the late-time universe even with the
simple choice of the Hubble horizon as the IR (infrared) cutoff. We provide
detailed descriptions of the cosmological evolution, showing how the fractional
calculus ingredients can alleviate quite a few issues associated with the
conventional HDE scenario. Concretely, we compute and plot diagrams using the
Hubble horizon cutoff for HDE. The density parameters for DE and dark matter
(DM), the deceleration parameter, and the DE EoS parameter indicate how the
universe may evolve within our FHDE model, fitting within an appropriate
scenario of late-time cosmology.
