Anomalous transport : foundations and applications

By Rainer Klages, G. Radons, Igor M. Sokolov. 2008

547 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9b874bed34280b3fd1342b33099b7a8f4802ded1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Well-posedness of Hamilton–Jacobi equations with Caputo’s time fractional derivative (2016, background): “Although many de nitions of a di erent kind of fractional derivatives have been suggested, we will not touch them in this paper and instead the reader is referred to [10, 14, 22, 23, 36, 38, 45].”
A unified Petrov-Galerkin spectral method for fractional PDEs (2015, background): “In these applications, fractional partial differential equations (FPDEs) appear of different type such as time- and/or space-fractional diffusion equation of parabolic nature [12], time- and/or space fractional advection, advection–diffusion and Burger’s equations of hyperbolic character [13,14], al”
Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions☆ (2011, background): “Furthermore, two kinds of Weyl fractional derivatives defined for periodic functions [20], namely the Weyl-Liouville and Weyl-Marchaud fractional derivatives, are also worth mentioning.”
Numerical solution of time fractional diffusion systems (2017, background): “Fractional models are increasingly used in many modelling situations including viscoelastic materials in mechanics [30, 42], anomalous diffusion in transport dynamics of complex systems [25, 33], soft tissues such as mitral valve in the human heart [40], some biological processes in rheology [12], t”
Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation (2013, background): “Fractional derivatives of order between zero and one are widely used in describing anomalous diffusion processes [3], while fractional diffusion-wave equations have applications in modeling universal electromagnetic, acoustic, and mechanical responses [4, 5].”
Conservation laws for time-fractional subdiffusion and diffusion-wave equations (2014, background): “, [33–39] and references therein) do not have a Lagrangian.”
On three explicit difference schemes for fractional diffusion and diffusion-wave equations (2009, unknown): “− f (0) 0(1 − γ ) t m − f (0) 0(2 − γ ) t m (8) for the CL method [25, 29].”
Fractional-order uniaxial visco-elasto-plastic models for structural analysis (2016, background): “For instance, it has been found that the transport dynamics in complex and/or disordered systems is governed by non-exponential relaxation patterns [6,7].”
FracFit: A robust parameter estimation tool for fractional calculus models (2017, background): “So-called anomalous transport is quite ubiquitous, spanning a multitude of scientific disciplines [Klages et al., 2008], including the hydrologic sciences where it has been observed in both surface [Deng et al., 2006; Phanikumar et al., 2007; Haggerty et al., 2002; Aubeneau et al., 2014] and…”