Fractional-order modeling and experimental validation of levofloxacin degradation in wastewater treatment systems
DOI: https://doi.org/10.3846/mma.2026.23545Abstract
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.
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fractional Caputo model, electro-fenton, levofloxacin, COD, ABM scheme, sensitivityHow to Cite
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Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
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References
M.S. Abdo, N. Alghamdi, H.Z. Alzumi and W. Shammakh. Fractional-order modeling of tuberculosis and diabetes mellitus co-existence dynamics. Comput. Biol. Med., 195:110514, 2025. https://doi.org/10.1016/j.compbiomed.2025.110514
A. Ahmadini, A. Msmali, Z. Mutum and Y.S. Raghav. The mathematical modeling approach for the wastewater treatment process in saudi arabia during covid-19 pandemic. Discrete Dyn. Nat. Soc., 2022:1061179, 2022. https://doi.org/10.1155/2022/1061179
M.A. Almalahi, S.K. Panchal, W. Shatanawi, M.S. Abdo and K. Shah. Analytical study of transmission dynamics of 2019-ncov pandemic via fractal fractional operator. Results Phys., 24:104045, 2021. https://doi.org/10.1016/j.rinp.2021.104045
Y.N. Anjam, M. Yavuz, M. Ur Rahman and A. Batool. Analysis of a fractional pollution model in a system of three interconnecting lakes. AIMS Biophys., 10(2):220–240, 2023. https://doi.org/10.3934/biophy.2023014
D. Baleanu, K. Diethelm, E. Scalas and J.J. Trujillo. Fractional Calculus: Models and Numerical Methods. World Scientific, 2012. https://doi.org/10.1142/8180
M. Barbu and E. Ceanga. Fractional order controllers for urban wastewater treatment systems. In Proc. 23rd Mediterranean Conf. Control Autom., pp. 1174–1179. IEEE, 2015. https://doi.org/10.1109/MED.2015.7158914
I. Dey, A.G. Sheik and S.R. Ambati. Fractional-order models identification and control within a supervisory control framework for efficient nutrients removal in biological wastewater treatment plants. Environ. Sci. Pollut. Res., 30(6):16642– 16660, 2023. https://doi.org/10.1007/s11356-022-23235-x
K. Diethelm. The Analysis of Fractional Differential Equations. Lecture Notes in Mathematics. Springer, 2010. https://doi.org/10.1007/978-3-642-14574-2
R. Hilfer(Ed.). Applications of Fractional Calculus in Physics. World Scientific, 2000. https://doi.org/10.1142/3779
M.B. Jeelani, A.S. Alnahdi, M.S. Abdo, M.A. Abdulwasaa, K. Shah and H.A. Wahash. Mathematical modeling and forecasting of covid-19 in saudi arabia under fractal-fractional derivative in caputo sense with power-law. Axioms, 10(3):228, 2021. https://doi.org/10.3390/axioms10030228
A.A. Kilbas, H.M. Srivastava and J.J. Trujillo. Theory and Applications of Fractional Differential Equations, volume 204 of North-Holland Mathematics Studies. Elsevier, 2006.
L. Martinez-Ayala, J. Bornacelli, M.A. Ojeda-Misses, J.A. Arano-Martinez, C. Torres-Torres and H. Martines-Arano. Chaos-driven detection of methylene blue in wastewater using fractional calculus and laser systems. Meas. Sci. Technol., 36(1):015801, 2024. https://doi.org/10.1088/1361-6501/ad817d
L. Meng, X. Zhang, A. Wei and X. Han. Fractional order control for aeration of activated sludge wastewater treatment processes. In Proc. 4th Int. Conf. Machinery, Materials and Information Technology Applications, pp. 1129–1135. Atlantis Press, 2017. https://doi.org/10.2991/icmmita-16.2016.264
R. Metzler and J. Klafter. The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A, 37(31):R161–R208, 2004. https://doi.org/10.1088/0305-4470/37/31/R01
S. Panjwani, E.S.S. Tejaswini and A.S. Rao. Fractional order model-based design of controllers for improved operation of wastewater treatment plants. Trans. Indian Natl. Acad. Eng., 5:719–726, 2020. https://doi.org/10.1007/s41403-020-00169-9
I. Podlubny. Fractional Differential Equations. Elsevier, 1999.
P. Priya and A. Sabarmathi. Caputo fractal fractional order derivative of soil pollution model due to industrial and agrochemical. Int. J. Appl. Comput. Math., 8(5):250, 2022. https://doi.org/10.1007/s40819-022-01431-0
A.H. Rabab, A.H. Afnan and S.Y. Muna. Effect of the cathode material on the efficiency of the electro-fenton process to remove pefloxacin: Kinetics and oxidation products. Environ. Prot. Eng., 50(2), 2024. https://doi.org/10.37190/epe240205
A.H. Rabab, S.Y. Muna, A.H. Afnan, K. Ghizlan and E. Mohamed. Grepafloxacin degradation and mineralization in water by electro-fenton process. Int. J. Electrochem. Sci., 19:100556, 2024. https://doi.org/10.1016/j.ijoes.2024.100556
A.H. Rabab, S.Y. Muna, E. Mohamed and A.H. Afnan. Comparative analysis and kinetic modeling of marbofloxacin degradation via electro-fenton and biodegradation optimization. Rocz. Ochr. Srod., 26:638–657, 2024. https://doi.org/10.54740/ros.2024.056
L. Sadek, D. Baleanu, M.S. Abdo and W. Shatanawi. Introducing novel thetafractional operators: Advances in fractional calculus. J. King Saud Univ. Sci., 36(9):103352, 2024. https://doi.org/10.1016/j.jksus.2024.103352
A.G. Sheik, I. Dey, S.R. Ambati, A. Kumar, S. Kumari and F. Bux. Integrated intelligent supervisory controller with fractional controller design for plant-wide wastewater treatment plants. Res. Square, 2023. https://doi.org/10.21203/rs.3.rs-3160354/v1
C. Da Silva, M. Peces, A. Jaques, J.J. Munoz, J. Dosta and S. Astals. Fractional calculus as a generalized kinetic model for biochemical methane potential tests. Bioresour. Technol., 396:130412, 2024. https://doi.org/10.1016/j.biortech.2024.130412
M.S. Yahya, S.H. Alotaibi, A.A. Hakami and N. Beqqal. Enhanced degradation of marbofloxacin via a synergistic photoelectro–fenton–peroxymonosulfate process: Kinetic and energy insights. J. Environ. Manage., 398:128544, 2026. https://doi.org/10.1016/j.jenvman.2026.128544
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Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
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