The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics

2,080 citations recorded by the source corpus.

How researchers see this paper

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

The blow-up and global existence of solutions of Cauchy problems for a time fractional diffusion equation (2015, neutral): “see [21], [25], [28], [18] and references therein.”
Time optimal boundary controls for the heat equation (2012, methodology): “31) involves a fractional power of the Dirichlet Laplacian, (−∆)θ, and it is used as mathematical model for physical processes exhibiting anomalously slow or fast diffusion (see, for instance, [10, 15]).”
Fractional wave equation and damped waves (2012, neutral): “For other interesting models in form of fractional differential equations we refer the reader to [3], [5], [9]-[12], [15]-[17], [20] to mention only few of many recent publications.”
A second-order accurate numerical method for the two-dimensional fractional diffusion equation (2007, methodology): “Fractional diffusion equations are used to model problems in physics (see a comprehensive review by Metzler and Klafter [25]), finance [10,16,28,31,30], and hydrology [2,4,5,32,33].”
Analytical solutions for the multi-term time–space Caputo–Riesz fractional advection–diffusion equations on a finite domain (2012, methodology): “The time, space and time–space fractional advection–dispersion equations have been used to describe important physical phenomena that arise in amorphous, colloid, glassy and porous media, in fractals and percolation clusters, comb structures, dielectrics and semiconductors, biological systems, polym”