Fractional Holographic Dark Energy Driven Reconstruction of $f(Q)$ Gravity and its Cosmological Implications

Abstract: In order to explain the late-time acceleration of the Universe, we present a reconstructed version of the $f(Q)$ gravity theory in this work, which is inspired by the integrating the fractional holographic dark energy with the Hubble horizon as the infrared cutoff. This reconstructed $f(Q)$ gravity model shows a geometrically motivated dark energy component and naturally recovers General Relativity in the appropriate limit. The free parameters of the model are constrained using the latest DESI BAO data, previous BAO compilations (P-BAO), and cosmic chronometer (CC) datasets through a Markov Chain Monte Carlo (MCMC) analysis. The reconstructed Hubble parameter $H(z)$ exhibits excellent consistency with observational data, with high values of $R^2$ and low values of $χ^2_{\min}$, AIC, and BIC, confirming the model's strong statistical performance relative to $Λ$CDM. With current $q(0) \in [-0.40, -0.32]$ and a transition redshift $z_{\text{tr}} \sim 0.56$--$0.72$, the dynamical diagnostics show a smooth transition from a decelerated to an accelerated phase. While the $Om(z)$ diagnostic exhibits a negative slope, indicating that the model is not $Λ$CDM, the effective equation-of-state parameter $ω{\text{eff}}(z)$ stays within the quintessence regime ($-1 < ω{\text{eff}} < -1/3$). The analysis of classical energy conditions shows that the WEC, DEC, and NEC are satisfied throughout the cosmic evolution, with a violation of the SEC at lower-redshift, which is consistent with late-time acceleration. Linear homogeneous perturbation analysis further confirms the model's dynamical stability. Conclusively, the FHDE-inspired reconstructed $f(Q)$ gravity provides a stable, observationally compatible, and geometrically motivated alternative to $Λ$CDM, that successfully describes the late-time cosmic acceleration within the symmetric teleparallel framework.