Fractional dark energy: Phantom behavior and negative absolute temperature

The fractional dark energy (FDE) model describes the accelerated expansion of Universe through a nonrelativistic gas particles with noncanonical kinetic term. This term is proportional to absolute value three-momentum power $3w$, where $w$ simply equation state parameter, and corresponding leads an density that mimics cosmological constant. In this paper we expand considering nonzero chemical potential show it may thermodynamically describe phantom regime. Planck constraints on parameter put upper limits allowed ratio temperature. second part, investigate system negative temperatures (NAT). NAT are possible in quantum systems cosmology, if there exists bound energy. maximum one ingredient FDE indicates connection between NAT, composed fermions. scenario, equal minus and, using observations, find transition from positive at any redshift larger than one.