A review of applications of fractional calculus in Earth system dynamics
Fractional calculus has been used to model various hydrologic processes for 15 years. Yet,
there are still major gaps between real-world hydrologic dynamics and fractional-order …
there are still major gaps between real-world hydrologic dynamics and fractional-order …
A review of applications of fractional advection–dispersion equations for anomalous solute transport in surface and subsurface water
Fractional advection–dispersion equations (FADEs) have been widely used in hydrological
research to simulate the anomalous solute transport in surface and subsurface water …
research to simulate the anomalous solute transport in surface and subsurface water …
A distributed-order time fractional derivative model for simulating bimodal sub-diffusion in heterogeneous media
Bimodal transport due to dual-mobile advection or mass exchange between mobile and
immobile zones has been widely observed for pollutants moving in heterogeneous media …
immobile zones has been widely observed for pollutants moving in heterogeneous media …
Boundary conditions for two-sided fractional diffusion
JF Kelly, H Sankaranarayanan… - Journal of Computational …, 2019 - Elsevier
This paper develops appropriate boundary conditions for the two-sided fractional diffusion
equation, where the usual second derivative in space is replaced by a weighted average of …
equation, where the usual second derivative in space is replaced by a weighted average of …
Backward particle tracking of anomalous transport in multi‐dimensional aquifers
Y Zhang - Water Resources Research, 2022 - Wiley Online Library
Backward particle tracking (BPT) remains a subject of research and applications in
hydrology for decades, and most BPT models and software suits assume Fickian diffusion …
hydrology for decades, and most BPT models and software suits assume Fickian diffusion …
Time fractional derivative model with Mittag-Leffler function kernel for describing anomalous diffusion: Analytical solution in bounded-domain and model comparison
Non-Fickian or anomalous diffusion had been well documented in material transport through
heterogeneous systems at all scales, whose dynamics can be quantified by the time …
heterogeneous systems at all scales, whose dynamics can be quantified by the time …
Impact of absorbing and reflective boundaries on fractional derivative models: Quantification, evaluation and application
Fractional-derivative models are promising tools for characterizing non-Fickian transport in
heterogeneous media. Most fractional models utilize an infinite domain, although realistic …
heterogeneous media. Most fractional models utilize an infinite domain, although realistic …
[HTML][HTML] Adjoint models with non-Fickian reactive transport to identify pollutant sources in water
Y Zhang - Journal of Hazardous Materials Advances, 2023 - Elsevier
Pollutant source identification (PSI) has remained a research topic in environmental
sciences for decades for hazardous chemicals, with the assumption that the transport of …
sciences for decades for hazardous chemicals, with the assumption that the transport of …
Efficient difference method for time-space fractional diffusion equation with Robin fractional derivative boundary condition
B Zhang, W Bu, A Xiao - Numerical Algorithms, 2021 - Springer
In this paper, a numerical method is proposed to solve the time-space fractional diffusion
equation with Robin fractional derivative boundary condition. Under the weak regularity …
equation with Robin fractional derivative boundary condition. Under the weak regularity …
A fast solver for spectral elements applied to fractional differential equations using hierarchical matrix approximation
We develop a fast solver for the spectral element method (SEM) applied to the two-sided
fractional diffusion equation on uniform, geometric and graded meshes. By approximating …
fractional diffusion equation on uniform, geometric and graded meshes. By approximating …