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Nonlocal Modeling and Inverse Parameter Estimation of Time-Varying Vehicular Emissions in Urban Pollution Dynamics

Author

Listed:
  • Muratkan Madiyarov

    (Department of Mathematics, Higher School of Information Technology and Natural Sciences, SarsenAmanzholov East Kazakhstan University, Oskemen 070000, Kazakhstan)

  • Nurlana Alimbekova

    (Department of Mathematics, Higher School of Information Technology and Natural Sciences, SarsenAmanzholov East Kazakhstan University, Oskemen 070000, Kazakhstan)

  • Aibek Bakishev

    (Department of Mathematics, Higher School of Information Technology and Natural Sciences, SarsenAmanzholov East Kazakhstan University, Oskemen 070000, Kazakhstan)

  • Gabit Mukhamediyev

    (Department of Mathematics, Higher School of Information Technology and Natural Sciences, SarsenAmanzholov East Kazakhstan University, Oskemen 070000, Kazakhstan)

  • Yerlan Yergaliyev

    (Department of Mathematics, Higher School of Information Technology and Natural Sciences, SarsenAmanzholov East Kazakhstan University, Oskemen 070000, Kazakhstan)

Abstract

This paper investigates the dispersion of atmospheric pollutants in urban environments using a fractional-order convection–diffusion-reaction model with dynamic line sources associated with vehicle traffic. The model includes Caputo fractional time derivatives and Riesz fractional space derivatives to account for memory effects and non-local transport phenomena characteristic of complex urban air flows. Vehicle trajectories are generated stochastically on the road network graph using Dijkstra’s algorithm, and each moving vehicle acts as a mobile line source of pollutant emissions. To reflect the daily variability of emissions, a time-dependent modulation function determined by unknown parameters is included in the source composition. These parameters are inferred by solving an inverse problem using synthetic concentration measurements from several fixed observation points throughout the area. The study presents two main contributions. Firstly, a detailed numerical analysis of how fractional derivatives affect pollutant dispersion under realistic time-varying mobile source conditions, and secondly, an evaluation of the performance of the proposed parameter estimation method for reconstructing time-varying emission rates. The results show that fractional-order models provide increased flexibility for representing anomalous transport and retention effects, and the proposed method allows for reliable recovery of emission dynamics from sparse measurements.

Suggested Citation

  • Muratkan Madiyarov & Nurlana Alimbekova & Aibek Bakishev & Gabit Mukhamediyev & Yerlan Yergaliyev, 2025. "Nonlocal Modeling and Inverse Parameter Estimation of Time-Varying Vehicular Emissions in Urban Pollution Dynamics," Mathematics, MDPI, vol. 13(17), pages 1-26, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2772-:d:1736558
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    References listed on IDEAS

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    1. Abdumauvlen Berdyshev & Dossan Baigereyev & Kulzhamila Boranbek, 2023. "Numerical Method for Fractional-Order Generalization of the Stochastic Stokes–Darcy Model," Mathematics, MDPI, vol. 11(17), pages 1-27, September.
    2. Goulart, A.G.O. & Lazo, M.J. & Suarez, J.M.S. & Moreira, D.M., 2017. "Fractional derivative models for atmospheric dispersion of pollutants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 9-19.
    3. Niraj Buyo & Akbar Sheikh-Akbari & Farrukh Saleem, 2025. "An Ensemble Approach to Predict a Sustainable Energy Plan for London Households," Sustainability, MDPI, vol. 17(2), pages 1-30, January.
    4. Dossan Baigereyev & Nurlana Alimbekova & Abdumauvlen Berdyshev & Muratkan Madiyarov, 2021. "Convergence Analysis of a Numerical Method for a Fractional Model of Fluid Flow in Fractured Porous Media," Mathematics, MDPI, vol. 9(18), pages 1-25, September.
    5. Miglena N. Koleva & Lubin G. Vulkov, 2023. "Numerical Solution of Fractional Models of Dispersion Contaminants in the Planetary Boundary Layer," Mathematics, MDPI, vol. 11(9), pages 1-21, April.
    6. Goulart, A.G. & Lazo, M.J. & Suarez, J.M.S., 2020. "A deformed derivative model for turbulent diffusion of contaminants in the atmosphere," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
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