Articles | Volume 21, issue 3
https://doi.org/10.5194/hess-21-1547-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Special issue:
https://doi.org/10.5194/hess-21-1547-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
13 Mar 2017
Research article |
| 13 Mar 2017
Governing equations of transient soil water flow and soil water flux in multi-dimensional fractional anisotropic media and fractional time
M. Levent Kavvas
CORRESPONDING AUTHOR
Hydrologic Research Laboratory, Department of Civil & Environmental
Engineering, University of California, Davis, CA 95616, USA
Ali Ercan
Hydrologic Research Laboratory, Department of Civil & Environmental
Engineering, University of California, Davis, CA 95616, USA
James Polsinelli
Hydrologic Research Laboratory, Department of Civil & Environmental
Engineering, University of California, Davis, CA 95616, USA
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Cited
23 citations as recorded by crossref.
- Modelling the dynamic poroelastic state of saturated–unsaturated soil considering non-local interactions V. Bohaienko & T. Blagoveshchenskaya 10.1007/s40324-024-00369-1
- Modelling solute dispersion in periodic heterogeneous porous media: Model benchmarking against intermediate scale experiments S. Majdalani et al. 10.1016/j.jhydrol.2018.03.024
- Numerical Evaluation of Fractional Vertical Soil Water Flow Equations A. Ercan & M. Kavvas 10.3390/w13040511
- Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time M. Kavvas et al. 10.5194/esd-11-1-2020
- Fractional derivative approach to non-Darcian flow in porous media H. Zhou & S. Yang 10.1016/j.jhydrol.2018.09.039
- A fractional derivative perspective on transient pulse test for determining the permeability of rocks S. Yang et al. 10.1016/j.ijrmms.2018.11.013
- Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time M. Kavvas et al. 10.5194/esd-8-921-2017
- Convergence analysis of a spectral numerical method for a peridynamic formulation of Richards’ equation F. Difonzo & S. Pellegrino 10.1016/j.matcom.2024.04.007
- A fast finite-difference algorithm for solving space-fractional filtration equation with a generalised Caputo derivative V. Bohaienko 10.1007/s40314-019-0878-5
- Identification of fractional water transport model with ψ-Caputo derivatives using particle swarm optimization algorithm V. Bohaienko et al. 10.1016/j.amc.2020.125665
- Generalizations of incompressible and compressible Navier–Stokes equations to fractional time and multi-fractional space M. Kavvas & A. Ercan 10.1038/s41598-022-20911-3
- A numerical method for a nonlocal form of Richards' equation based on peridynamic theory M. Berardi et al. 10.1016/j.camwa.2023.04.032
- Exploring Integral ϝ-Contractions with Applications to Integral Equations and Fractional BVPs Z. Nisar et al. 10.3390/fractalfract7120833
- Using a shifted Grünwald‐Letnikov scheme for the Caputo derivative to study anomalous solute transport in porous medium P. Mascarenhas et al. 10.1002/nag.2936
- Fractional derivative method for anomalous aquitard flow in a leaky aquifer system with depth-decaying aquitard hydraulic conductivity Y. Li et al. 10.1016/j.watres.2023.120957
- Stochastic Foundation to Solving Transient Unsaturated Flow Problems Using a Fractional Dispersion Term P. Mascarenhas & A. Cavalcante 10.1061/(ASCE)GM.1943-5622.0002251
- Numerical simulation of irrigation scheduling using fractional Richards equation M. Romashchenko et al. 10.1007/s00271-021-00725-3
- Conceptual principles of water resources management in irrigated agriculture M. Romashchenko et al. 10.5194/piahs-385-111-2024
- Time–space fractional governing equations of one‐dimensional unsteady open channel flow process: Numerical solution and exploration A. Ercan & M. Kavvas 10.1002/hyp.11240
- Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation T. Tu et al. 10.1002/hyp.11500
- Conceptual principles of watering control under irrigation M. Romashchenko et al. 10.31073/mivg202201-328
- Temperature and plant root effects on soil hydrological response and slope stability J. Ni et al. 10.1016/j.compgeo.2024.106663
- Selection of ψ-Caputo derivatives’ functional parameters in generalized water transport equation by genetic programming technique V. Bohaienko 10.1016/j.rico.2021.100068
23 citations as recorded by crossref.
- Modelling the dynamic poroelastic state of saturated–unsaturated soil considering non-local interactions V. Bohaienko & T. Blagoveshchenskaya 10.1007/s40324-024-00369-1
- Modelling solute dispersion in periodic heterogeneous porous media: Model benchmarking against intermediate scale experiments S. Majdalani et al. 10.1016/j.jhydrol.2018.03.024
- Numerical Evaluation of Fractional Vertical Soil Water Flow Equations A. Ercan & M. Kavvas 10.3390/w13040511
- Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time M. Kavvas et al. 10.5194/esd-11-1-2020
- Fractional derivative approach to non-Darcian flow in porous media H. Zhou & S. Yang 10.1016/j.jhydrol.2018.09.039
- A fractional derivative perspective on transient pulse test for determining the permeability of rocks S. Yang et al. 10.1016/j.ijrmms.2018.11.013
- Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time M. Kavvas et al. 10.5194/esd-8-921-2017
- Convergence analysis of a spectral numerical method for a peridynamic formulation of Richards’ equation F. Difonzo & S. Pellegrino 10.1016/j.matcom.2024.04.007
- A fast finite-difference algorithm for solving space-fractional filtration equation with a generalised Caputo derivative V. Bohaienko 10.1007/s40314-019-0878-5
- Identification of fractional water transport model with ψ-Caputo derivatives using particle swarm optimization algorithm V. Bohaienko et al. 10.1016/j.amc.2020.125665
- Generalizations of incompressible and compressible Navier–Stokes equations to fractional time and multi-fractional space M. Kavvas & A. Ercan 10.1038/s41598-022-20911-3
- A numerical method for a nonlocal form of Richards' equation based on peridynamic theory M. Berardi et al. 10.1016/j.camwa.2023.04.032
- Exploring Integral ϝ-Contractions with Applications to Integral Equations and Fractional BVPs Z. Nisar et al. 10.3390/fractalfract7120833
- Using a shifted Grünwald‐Letnikov scheme for the Caputo derivative to study anomalous solute transport in porous medium P. Mascarenhas et al. 10.1002/nag.2936
- Fractional derivative method for anomalous aquitard flow in a leaky aquifer system with depth-decaying aquitard hydraulic conductivity Y. Li et al. 10.1016/j.watres.2023.120957
- Stochastic Foundation to Solving Transient Unsaturated Flow Problems Using a Fractional Dispersion Term P. Mascarenhas & A. Cavalcante 10.1061/(ASCE)GM.1943-5622.0002251
- Numerical simulation of irrigation scheduling using fractional Richards equation M. Romashchenko et al. 10.1007/s00271-021-00725-3
- Conceptual principles of water resources management in irrigated agriculture M. Romashchenko et al. 10.5194/piahs-385-111-2024
- Time–space fractional governing equations of one‐dimensional unsteady open channel flow process: Numerical solution and exploration A. Ercan & M. Kavvas 10.1002/hyp.11240
- Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation T. Tu et al. 10.1002/hyp.11500
- Conceptual principles of watering control under irrigation M. Romashchenko et al. 10.31073/mivg202201-328
- Temperature and plant root effects on soil hydrological response and slope stability J. Ni et al. 10.1016/j.compgeo.2024.106663
- Selection of ψ-Caputo derivatives’ functional parameters in generalized water transport equation by genetic programming technique V. Bohaienko 10.1016/j.rico.2021.100068
Latest update: 29 Jul 2025
Short summary
In this study dimensionally consistent governing equations of continuity and motion for transient soil water flow and water flux in fractional time and in fractional multiple space dimensions in anisotropic media are developed. By the introduction of the Brooks–Corey constitutive relationships, an explicit form of the equations is obtained. The developed governing equations, in their fractional time but integer space forms, show behavior consistent with the previous experimental observations.
In this study dimensionally consistent governing equations of continuity and motion for...
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