Fractional-order modeling and experimental validation of levofloxacin degradation in wastewater treatment systems

This work develops and experimentally validates a Caputo fractional-order model for levofloxacin degradation and Chemical Oxygen Demand (COD) mineralization in Electro-Fenton wastewater treatment, capturing memory effects in long-time mineralization dynamics. Stability analysis using Lyapunov methods demonstrated asymptotic convergence to the equilibrium point. The system is solved using the Adams-Bashforth-Moulton (ABM) scheme, and parameters are calibrated via grid search over α with constrained kinetic optimization. The optimal orders indicate stronger memory in COD removal (α⋆ = 0.7) than in levofloxacin decay (α⋆ = 0.9), achieving high agreement with experiments (R2 = 0.9192 for Levofloxacin and R2 = 0.9974 for COD) across varying electrolyte, pH, catalyst, and biodegradability conditions. Relative to the integer-order model, the fractional model reduces residual error, and accurately predicts levofloxacin decay and COD mineralization under optimized conditions, highlighting the biodegradability potential of the treated wastewater. Finally, local sensitivity analysis identifies fractional order α and nonlinear reaction order n as the most influential parameters for predictive accuracy and process optimization.