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1981, CBMS-NSF regional conference series in applied mathematics, ISBN 089871169X, Volume 36, 75
Book
Journal of Computational Physics, ISSN 0021-9991, 2007, Volume 225, Issue 2, pp. 1533 - 1552
In this paper, we consider the numerical resolution of a time-fractional diffusion equation, which is obtained from the standard diffusion equation by... 
Fractional diffusion equation | Spectral approximation | Stability | Convergence | ORDER | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | WAVE EQUATION | spectral approximation | convergence | fractional diffusion equation | PHYSICS, MATHEMATICAL | stability
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 06/2015, Volume 289, pp. 60 - 78
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 01/2018, Volume 264, Issue 1, pp. 378 - 424
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 06/2016, Volume 299, pp. 159 - 175
In this paper, a series of new high-order numerical approximations to th order Caputo derivative is constructed by using th degree interpolation approximation... 
Difference scheme | Advection–diffusion equation | Caputo derivative | Convergence | Advection-diffusion equation | MATHEMATICS, APPLIED | Approximation | Mathematical analysis | Dirichlet problem | Truncation errors | Mathematical models | Derivatives
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 07/2015, Volume 84, Issue 294, pp. 1703 - 1727
A class of second order approximations, called the weighted and shifted Grünwald difference (WSGD) operators, are proposed for Riemann-Liouville fractional... 
Weighted and shifted grünwald difference (WSGD) operator | Riemann-Liouville fractional derivative | Fractional diffusion equation | MATHEMATICS, APPLIED | NUMERICAL-METHOD | Weighted and shifted Grunwald difference (WSGD) operator
Journal Article
Monthly Notices of the Royal Astronomical Society, ISSN 0035-8711, 11/2012, Volume 427, Issue 1, pp. 415 - 427
Journal Article
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-503X, 08/2009, Volume 367, Issue 1901, pp. 3157 - 3171
Biased diffusive transport of Brownian particles through irregularly shaped, narrow confining quasi-one-dimensional structures is investigated. The complexity... 
Brownian motion | Entropic transport | Fick-Jacobs equation | MULTIDISCIPLINARY SCIENCES | SILICON | DIFFUSION | CHANNELS | BROWNIAN MOTORS | entropic transport | STOCHASTIC RESONANCE | Probability | Entropy | Models, Chemical | Diffusion
Journal Article
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, ISSN 0035-8711, 05/2019, Volume 485, Issue 2, pp. 1635 - 1650
In the theory of cosmic rays we use diffusive transport equations to model the motion of energetic particles through space. A more fundamental description can... 
diffusion | TRANSPORT | magnetic fields | MAGNETIC SLAB TURBULENCE | ASTRONOMY & ASTROPHYSICS | ENERGETIC CHARGED-PARTICLES | MEAN FREE-PATH | turbulence | ANALYTIC CALCULATION
Journal Article
by Chen, S and Liu, F and Zhuang, P and Anh, V
Applied Mathematical Modelling, ISSN 0307-904X, 2009, Volume 33, Issue 1, pp. 256 - 273
The fractional Fokker–Planck equation has been used in many physical transport problems which take place under the influence of an external force field. In... 
The energy method | Finite difference approximation | Stability | Fractional Fokker–Planck equation | Fractional Fokker-Planck equation | ANOMALOUS DIFFUSION | TRANSPORT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | RELAXATION | SYSTEMS | MEDIA
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 01/2019, Volume 118, pp. 58 - 64
To solve the problems of non-local dynamical systems, Caputo and Fabrizio proposed a new definition for the fractional derivative. Atangana and Baleanu... 
Fractional Advection-Diffusion equation | Atangana–Baleanu derivative | Finite difference method | Atangana-Baleanu derivative | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | FRACTIONAL CALCULUS | DIFFERENTIAL-EQUATIONS | DIFFUSION | PHYSICS, MATHEMATICAL
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 02/2015, Volume 275, pp. 216 - 227
In this paper an implicit scheme for the numerical approximation of the distributed order time-fractional reaction–diffusion equation with a nonlinear source... 
Fractional differential equation | Distributed order equation | Diffusion equation | Implicit finite difference method | Caputo derivative | SCHEME | MATHEMATICS, APPLIED | TIME-FRACTIONAL DIFFUSION | FINITE-DIFFERENCE METHODS | STABILITY
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 06/2016, Volume 35, Issue C, pp. 69 - 87
We present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional... 
Fractional variable order | Fractional differential equations | Approximation methods |