A Hybrid Numerical Approach for the Analysis of Fractional Advection–Diffusion Models in Atmospheric Pollution

Air pollution has emerged as one of the major environmental concerns worldwide due to its adverse effects on human health, ecosystems, and climate. The transport and dispersion of atmospheric pollutants are commonly described using the classical advection–diffusion equation (ADE), which accounts for the movement of contaminants through advection caused by wind and diffusion driven by concentration gradients. However, in realistic atmospheric environments characterized by turbulence, heterogeneity, and memory-dependent transport mechanisms, the classical ADE often fails to accurately represent the observed anomalous diffusion behaviour. In such situations, Fractional Advection–Diffusion Equations (FADEs) provide a more suitable framework by incorporating fractional derivatives to capture long-range interactions and memory effects associated with non-Gaussian diffusion processes. In this work, we consider a one-dimensional time-fractional advection-diffusion equation to model the dispersion of air pollutants under anomalous diffusion conditions. The Caputo fractional derivative is employed to describe the temporal memory effects inherent in the transport process. The principal contribution of this study is the successful implementation of the Jafari new iterative technique (JNIT) for solving the time-fractional advection–diffusion equation arising in atmospheric pollution modelling. The effectiveness, simplicity, and computational efficiency of the proposed method are demonstrated through illustrative examples. The obtained results reveal that the JNIT provides accurate approximate solutions with rapid convergence and reduced computational complexity, making it a promising tool for investigating a wide class of fractional partial differential equations encountered in environmental and engineering applications.