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Journal of Computational Physics, ISSN 0021-9991, 2011, Volume 230, Issue 21, pp. 7830 - 7839
► We develop a fast alternating-direction method for fractional diffusion equations. ► This method reduces computational complexity from O( N 3) to O( N log... 
Fractional diffusion equation | Alternating-direction method | Toeplitz matrix | Anomalous diffusion | Circulant matrix | Fast Fourier transform | Accuracy | Computation | Gaussian elimination | Mathematical analysis | Differential equations | Mathematical models | Diffusion | Finite difference method
Journal Article
Physics Reports, ISSN 0370-1573, 11/2017, Volume 716-717, pp. 1 - 58
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental... 
Markov chain | Diffusion | Random walk | Point process | Network | GRAPH | STATISTICAL-MECHANICS | PHYSICS, MULTIDISCIPLINARY | COALESCING RANDOM-WALKS | ANOMALOUS DIFFUSION | 1ST-PASSAGE TIMES | COMMUNITY STRUCTURE | MODELS | COVER TIME | HEAT KERNEL | COMPLEX NETWORKS | Markov processes | Analysis
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 2015, Volume 80, Issue 1-2, pp. 281 - 286
Journal Article
Nature Materials, ISSN 1476-1122, 2012, Volume 11, Issue 6, pp. 481 - 485
It is commonly presumed that the random displacements that particles undergo as a result of the thermal jiggling of the environment follow a normal, or... 
ANOMALOUS DIFFUSION | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | FLUCTUATIONS | MATERIALS SCIENCE, MULTIDISCIPLINARY | DYNAMICS | CHEMISTRY, PHYSICAL | Materials science | Diffusion | Normal distribution | Brownian movements
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 2010, Volume 229, Issue 21, pp. 8095 - 8104
Fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not be modeled accurately by the second-order diffusion equations.... 
Fractional diffusion equations | Circulant and Toeplitz matrices | Fast finite difference methods | Anomalous diffusion | Fast Fourier transform
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 11/2008, Volume 78, Issue 5, p. 051106
We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered alpha-stable processes. The tempering results in... 
ANOMALOUS DIFFUSION | MODELS | PHYSICS, FLUIDS & PLASMAS | DISPERSION | DYNAMICS | CONVERGENCE | TIME | PHYSICS, MATHEMATICAL
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 01/2013, Volume 87, Issue 1, p. 012123
Journal Article
Physical Review Letters, ISSN 0031-9007, 03/2014, Volume 112, Issue 10, p. 108301
Large-scale molecular dynamics simulations show that nanoparticle (NP) diffusivity in weakly interacting mixtures of NPs and polymer melts has two very... 
ANOMALOUS DIFFUSION | MOLECULAR-DYNAMICS | SUBDIFFUSION | ACTIN NETWORKS | PHYSICS, MULTIDISCIPLINARY | SEMIDILUTE | VISCOSITY | NANOSCALE | SIMULATIONS | MELTS | BREAKDOWN
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 01/2017, Volume 465, pp. 562 - 572
In this paper, using the fractional operators with Mittag-Leffler kernel in Caputo and Riemann–Liouville sense the space–time fractional diffusion equation is... 
Integral transform operator | Fractional diffusion equation | Atangana–Baleanu fractional derivative | Anomalous diffusion | Subdiffusion | Atangana-Baleanu fractional derivative | TRANSPORT | APPROXIMATION | PHYSICS, MULTIDISCIPLINARY | MODEL
Journal Article