A review of applications of fractional calculus in Earth system dynamics

DOI10.1016/j.chaos.2017.03.051zbMath1374.86028OpenAlexW2605056791MaRDI QIDQ1677746

Harold H. Stowell, Yong Zhang, Mohsen Zayernouri, Samantha E. Hansen, Hong-Guang Sun

Publication date: 13 November 2017

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2017.03.051

zbMATH Keywords

fractional calculushydrologic processesfractional derivative modelssolid Earth

Mathematics Subject Classification ID

Hydrology, hydrography, oceanography (86A05) PDEs with randomness, stochastic partial differential equations (35R60) Research exposition (monographs, survey articles) pertaining to geophysics (86-02)

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Cites Work

• Unnamed Item
• Unnamed Item
• Flow of fractal fluid in pipes: non-integer dimensional space approach
• Water wave propagation in unbounded domains. II: Numerical methods for fractional PDEs
• Parameter estimation for operator scaling random fields
• Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation
• Homotopy perturbation method for a limit case Stefan problem governed by fractional diffusion equation
• Matrix approach to discrete fractional calculus. II: Partial fractional differential equations
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Mixing-driven equilibrium reactions in multidimensional fractional advection-dispersion systems
• Variable order and distributed order fractional operators
• Multi-order fractional differential equations and their numerical solution
• Nonequilibrium statistical mechanics of preasymptotic dispersion
• Fractional diffusion on bounded domains
• Distributed-order fractional diffusions on bounded domains
• Distributed order calculus and equations of ultraslow diffusion
• Forum: the state of stochastic hydrology
• On application of stochastic modeling of groundwater flow and transport
• Stochastic groundwater models in practice
• Stochastic hydrology: practical alternatives exist
• A sociological approach to the state of stochastic hydrogeology
• A rational role for stochastic concepts in subsurface hydrology: a personal perspective
• Stochastic hydrogeology -- challenges and misconceptions
• On the application of stochastic approaches in hydrogeology
• On certain stochastic hydrology issues
• The role of stochastic hydrogeological modeling in real-world engineering applications
• Dynamics of surface roughening in the space-fractional Kardar–Parisi–Zhang growth: numerical results
• Hydromagnetic Dynamo Theory
• Dynamic Scaling of Growing Interfaces
• Reflected spectrally negative stable processes and their governing equations
• A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
• Numerical investigation of 2D convection with extremely large viscosity variations
• Mechanics with variable-order differential operators
• Towards a deterministic KPZ equation with fractional diffusion: the stationary problem
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• Integration and differentiation to a variable fractional order
• A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis
• Fractional diffusion in inhomogeneous media
• DISTRIBUTED ORDER FRACTIONAL SUB-DIFFUSION
• The growth of crystals and the equilibrium structure of their surfaces
• The random walk's guide to anomalous diffusion: A fractional dynamics approach