Time Fractional Diffusion: A Discrete Random Walk Approach
By Rudolf Gorenflo, Francesco Mainardi, Daniele Moretti, Paolo Paradisi. 2002
393 citations recorded by the source corpus.
Subfields: Modeling and Simulation, Molecular Biology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b619185918be3076c0ee6be7f10ea43cda6600d2
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Modeling and Simulation
- Fawang Liu
- Ian L Turner
- Chuanju Xu
- Vo Anh
- Weihua Deng
- G. Em Karniadakis
- Changpin Li
- Francesco Mainardi
In Molecular Biology
- Chuanju Xu
- Yuriy Povstenko
- Weihua Deng
- William McLean
- Yumin Lin
- Xianjuan Li
- Vidar Thomée
- G. Em Karniadakis
In Statistical and Nonlinear Physics
- Yuriy Povstenko
- Chuanju Xu
- Weihua Deng
- William McLean
- Xianjuan Li
- Yumin Lin
- Vidar Thomée
- Gianni Pagnini
Citations in the corpus
- High-order finite element methods for time-fractional partial differential equations (2011, background): “, in [1,2] and [3]) and thus the solutions of the equations become increasingly popular (see e.”
- Finite Element Method for the Space and Time Fractional Fokker-Planck Equation (2008, methodology): “For the numerical algorithms of the time fractional Fokker-Planck-type equation and the space fractional Fokker-Planck-type equation, there is already some progress covering the finite difference method, the finite element method, and some random approaches [11, 12, 13, 15, 18, 27, 28, 32, 40], Howe”
- Fractional Calculus as a Mathematical Tool to Improve the Modeling of Mass Transfer Phenomena in Food Processing (2012, background): “It has been shown [32, 40] that how this could be”
- Finite difference/spectral approximations for the time-fractional diffusion equation (2007, methodology): “[8,9] used the similarity method and the method of Laplace transform to obtain the scale-invariant solution of TFDE in terms of the wright function.”
- Discrete random walk models for space-time fractional diffusion (2002, methodology): “We find it convenient to proceed by steps: we first consider the case of the strictly time fractional diffusion, see also [26], and then, by combining these arguments with those for strictly space fractional diffusion, we treat the strictly space-time fractional diffusion.”
- Cauchy problem for fractional diffusion equations (2003, background): “For connections to statistical mechanics see also [11, 17].”
- Thermoelasticity that uses fractional heat conduction equation (2009, methodology): “In this paper, we consider a constitutive equation with “long-tale” power time-nonlocal kernel (see also [21, 26 ]), namely,”
- The -Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey (2010, neutral): “[7, 8, 9], [20, 21], [29, 30], [71].”
- A Fourier method for the fractional diffusion equation describing sub-diffusion (2007, background): “that accounts for spatial and temporal non-locality [5].”
- A Space-Time Spectral Method for the Time Fractional Diffusion Equation (2009, methodology): “[9, 10] used the similarity method and the method of Laplace transform to obtain the scale-invariant solution of TFDE in terms of the wright function.”
- Fractional-order uniaxial visco-elasto-plastic models for structural analysis (2016, methodology): “[19] adopted a finite-difference scheme by which they could generate discrete models of random walk in such anomalous diffusion.”
- Numerical solution via Laplace transforms of a fractional order evolution equation (2010, methodology): “The methods are combined with finite element discretization in the spatial variables to yield fully discrete methods.”