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Applied Mathematics Letters, ISSN 0893-9659, 04/2020, Volume 102, p. 106107
The extension of fractional power series solutions for linear fractional differential equations with variable coefficients is considered. Generalized series... 
Fractional differential equations | Fractional power series | Variable coefficients | Riemann–Liouville derivatives
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 07/2019, Volume 526, p. 121002
We construct a time-fractional geometric Fokker–Planck equation from the diffusion limit of a continuous time random walk with a power law waiting time... 
Geometric Brownian motion | Continuous time random walks | Anomalous diffusion | Subdiffusion | Fractional Fokker–Planck equation | Fractional Fokker-Planck equation | PHYSICS, MULTIDISCIPLINARY | FINANCE | MASTER-EQUATIONS
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 11/2018, Volume 372, pp. 373 - 384
•Provides a Monte Carlo method for simulating a DTRW with Sibuya waiting times.•This is more efficient than direct calculation for small anomalous... 
Monte Carlo | Discrete time random walk | Fractional calculus | Anomalous diffusion | DIGAMMA | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | STABILITY | DYNAMICS | PHYSICS, MATHEMATICAL | FRACTIONAL DIFFUSION EQUATION | Monte Carlo method | Stochastic processes | Differential equations | Mathematics - Numerical Analysis
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 03/2017, Volume 73, Issue 6, pp. 1315 - 1324
In the standard continuous time random walk the initial state is taken as a non-equilibrium state, in which the random walking particle has just arrived at a... 
Fokker–Planck equations | Fractional diffusion | Continuous time random walks | MATHEMATICS, APPLIED | Fokker-Planck equations | DIFFUSION
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 06/2016, Volume 452, pp. 86 - 93
Fractional-order SIR models have become increasingly popular in the literature in recent years, however unlike the standard SIR model, they often lack a... 
SIR models | Epidemiological models | Fractional order differential equations | Continuous time random walk | PHYSICS, MULTIDISCIPLINARY | RANDOM-WALKS | MATHEMATICAL-THEORY | Stochastic processes | Analysis | Models | Differential equations | Mathematical analysis | Compartments | Derivation | Mathematical models | Derivatives | Standards
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 09/2017, Volume 102, pp. 175 - 183
A generalised advection equation with a time fractional derivative is derived from a continuous time random walk on a one-dimensional lattice, with power law... 
Fractional diffusion | Discrete time random walks | Continuous time random walks | DYNAMICS APPROACH | PHYSICS, MULTIDISCIPLINARY | MASTER-EQUATIONS | PHYSICS, MATHEMATICAL | FOKKER-PLANCK EQUATIONS | ANOMALOUS ELECTRODIFFUSION | TRANSPORT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MODELS | RANDOM-WALKS | DOMAIN SOLUTIONS | Stochastic processes
Journal Article
Bulletin of Mathematical Biology, ISSN 0092-8240, 03/2016, Volume 78, Issue 3, pp. 468 - 499
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 03/2013, Volume 87, Issue 3
We derive the generalized master equation for reaction-diffusion on networks from an underlying stochastic process, the continuous time random walk (CTRW). The... 
TRANSPORT | INSTABILITY | PHYSICS, FLUIDS & PLASMAS | REACTION-DIFFUSION SYSTEMS | DYNAMICS | MEDIA | TURING PATTERNS | MODEL | PHYSICS, MATHEMATICAL
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 03/2017, Volume 73, Issue 6, pp. 1053 - 1062
Here we present a numerical method for the solution of time fractional partial differential equations (fPDEs). The method is based on constructing a sequence... 
Fractional differential equations | Integrablization | EQUATIONS | MATHEMATICS, APPLIED | FINITE-DIFFERENCE METHOD | STABILITY
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 07/2015, Volume 293, pp. 53 - 69
Journal Article
SIAM Journal on Applied Mathematics, ISSN 0036-1399, 2015, Volume 75, Issue 4, pp. 1445 - 1468
Journal Article
Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, 2013, Volume 8, Issue 2, pp. 17 - 27
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 08/2013, Volume 88, Issue 2, p. 022811
We have investigated the transport of particles moving as random walks on the vertices of a network, subject to vertex- and time-dependent forcing. We have... 
ANOMALOUS DIFFUSION | MODELS | SMALL-WORLD | CHEMOTAXIS | PHYSICS, FLUIDS & PLASMAS | ACTIVATOR-INHIBITOR SYSTEMS | DYNAMICS | TURING PATTERNS | PHYSICS, MATHEMATICAL | AGGREGATION
Journal Article
Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, 2017, Volume 12, Issue 6, pp. 23 - 36
Journal Article
Physical Review E, ISSN 2470-0045, 10/2017, Volume 96, Issue 4
The ubiquity of subdiffusive transport in physical and biological systems has led to intensive efforts to provide robust theoretical models for this phenomena.... 
ANOMALOUS DIFFUSION | TIME RANDOM-WALKS | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS | PLASMA-MEMBRANE
Journal Article
Fractal and Fractional, ISSN 2504-3110, 11/2017, Volume 1, Issue 1, p. 11
Journal Article
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