Abstract
We investigate the thermodynamic and phenomenological implications of a cosmological model governed by fractional entropy applied to the apparent horizon of a flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. By utilizing the unified first law of thermodynamics alongside the Kodama-Hayward temperature, we derive a generalized set of Friedmann equations characterized by a fractional parameter α ∈ (1, 2]. The thermodynamic analysis reveals that the specific heats CV and Cp share the same sign and depend solely on the deceleration parameter, demonstrating that the fractional model is thermodynamically stable during the late-time accelerated expansion and does not exhibit phase transitions. To constrain the background dynamics, we confront the truncated fractional model with a joint sample of late-time observational data, including Cosmic Chronometers, Pantheon+SH0ES supernovae, and the latest DESI DR2 Baryon Acoustic Oscillations. Exploring the physically motivated range 1 < α ≤ 2, we find that the fit quality degrades monotonically as α decreases from the General Relativity limit. Rather than limiting the model’s physical value, this demonstrates its theoretical robustness: the fractional framework acts as a continuous deformation parameter that preserves macroscopic thermodynamic stability. The data favors α close to 2 (yielding H0=69.50±0.42 km/s/Mpc and Ωm0=0.292±0.008), revealing that while the late-time background expansion strongly constrains deviations from the standard area law, the fractional model smoothly and stably accommodates these constraints without exhibiting thermodynamic pathologies.