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

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

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

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

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

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

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

Over the past several decades, there has been a proliferation of epidemiological models with ordinary derivatives replaced by fractional derivatives in an ad...

Epidemiological models | SIR model | Fractional calculus | TIME RANDOM-WALKS | INFECTIOUS-DISEASES | EPIDEMIC MODEL | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | EQUATIONS | DYNAMICS | ENDEMICITY | MATHEMATICAL-THEORY | Mathematical Concepts | Stochastic Processes | Communicable Diseases - epidemiology | Models, Biological | Humans | Epidemics - statistics & numerical data | Chronic diseases | Models | Epidemiology | Analysis

Epidemiological models | SIR model | Fractional calculus | TIME RANDOM-WALKS | INFECTIOUS-DISEASES | EPIDEMIC MODEL | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | EQUATIONS | DYNAMICS | ENDEMICITY | MATHEMATICAL-THEORY | Mathematical Concepts | Stochastic Processes | Communicable Diseases - epidemiology | Models, Biological | Humans | Epidemics - statistics & numerical data | Chronic diseases | Models | Epidemiology | Analysis

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

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

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

The continuous time random walk, introduced in the physics literature by Montroll and Weiss, has been widely used to model anomalous diffusion in external...

Continuous time random walk | Fractional diffusion | Fractional Fokker-Planck equation | Anomalous diffusion | Finite difference method | FOKKER-PLANCK EQUATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | STABILITY | SPINES | PHYSICS, MATHEMATICAL | Numerical analysis | Mathematical analysis | Random walk | Evolution | Mathematical models | Calculus | Diffusion | Probability density functions

Continuous time random walk | Fractional diffusion | Fractional Fokker-Planck equation | Anomalous diffusion | Finite difference method | FOKKER-PLANCK EQUATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | STABILITY | SPINES | PHYSICS, MATHEMATICAL | Numerical analysis | Mathematical analysis | Random walk | Evolution | Mathematical models | Calculus | Diffusion | Probability density functions

Journal Article

SIAM Journal on Applied Mathematics, ISSN 0036-1399, 2015, Volume 75, Issue 4, pp. 1445 - 1468

Continuous time random walks, which generalize random walks by adding a stochastic time between jumps, provide a useful description of stochastic transport at...

Limit theorems | Generalized master equation | Continuous time random walk | Fractional Fokker-Planck equation | Fractional calculus | Anomalous diffusion | MATHEMATICS, APPLIED | fractional calculus | DIFFERENTIAL-EQUATIONS | limit theorems | DIFFUSION EQUATION | fractional Fokker-Planck equation | ANOMALOUS ELECTRODIFFUSION | TRANSPORT | MODELS | continuous time random walk | generalized master equation | DOMAIN SOLUTIONS | MEDIA | anomalous diffusion

Limit theorems | Generalized master equation | Continuous time random walk | Fractional Fokker-Planck equation | Fractional calculus | Anomalous diffusion | MATHEMATICS, APPLIED | fractional calculus | DIFFERENTIAL-EQUATIONS | limit theorems | DIFFUSION EQUATION | fractional Fokker-Planck equation | ANOMALOUS ELECTRODIFFUSION | TRANSPORT | MODELS | continuous time random walk | generalized master equation | DOMAIN SOLUTIONS | MEDIA | anomalous diffusion

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2016, Volume 307, pp. 508 - 534

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations...

Fractional diffusion | Continuous time random walk | Discrete time random walk | Anomalous diffusion | Fractional reaction diffusion | Finite difference method | FOKKER-PLANCK EQUATION | APPROXIMATION | STABILITY | DIFFUSION EQUATION | PHYSICS, MATHEMATICAL | ACCURACY | TRANSPORT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | RANDOM-WALKS | Computer science | Analysis | Methods | Differential equations | Stochastic processes | Numerical analysis | Partial differential equations | Mathematical analysis | Consistency | Evolution | Mathematical models | Constraining | FINITE DIFFERENCE METHOD | RANDOMNESS | DIFFUSION EQUATIONS | PROBABILITY | STOCHASTIC PROCESSES | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | DIFFUSION | GRAPH THEORY

Fractional diffusion | Continuous time random walk | Discrete time random walk | Anomalous diffusion | Fractional reaction diffusion | Finite difference method | FOKKER-PLANCK EQUATION | APPROXIMATION | STABILITY | DIFFUSION EQUATION | PHYSICS, MATHEMATICAL | ACCURACY | TRANSPORT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | RANDOM-WALKS | Computer science | Analysis | Methods | Differential equations | Stochastic processes | Numerical analysis | Partial differential equations | Mathematical analysis | Consistency | Evolution | Mathematical models | Constraining | FINITE DIFFERENCE METHOD | RANDOMNESS | DIFFUSION EQUATIONS | PROBABILITY | STOCHASTIC PROCESSES | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | DIFFUSION | GRAPH THEORY

Journal Article

Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, 2013, Volume 8, Issue 2, pp. 17 - 27

One of the central results in Einstein's theory of Brownian motion is that the mean square displacement of a randomly moving Brownian particle scales linearly...

Fokker-Planck equation | Fractional diffusion | Stochastic process | Random walk | Reaction-diffusion | DERIVATION | ELECTRODIFFUSION | MEMBRANE | MULTIDISCIPLINARY SCIENCES | stochastic process | random walk | ANOMALOUS DIFFUSION | reaction-diffusion | TRANSPORT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | fractional diffusion | CABLE EQUATION MODELS | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | Mathematical models | Random walk theory | Diffusion | Brownian movements

Fokker-Planck equation | Fractional diffusion | Stochastic process | Random walk | Reaction-diffusion | DERIVATION | ELECTRODIFFUSION | MEMBRANE | MULTIDISCIPLINARY SCIENCES | stochastic process | random walk | ANOMALOUS DIFFUSION | reaction-diffusion | TRANSPORT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | fractional diffusion | CABLE EQUATION MODELS | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | Mathematical models | Random walk theory | Diffusion | Brownian movements

Journal Article

Bulletin of Mathematical Biology, ISSN 0092-8240, 5/2013, Volume 75, Issue 5, pp. 774 - 795

We have developed a mathematical model for in-host virus dynamics that includes spatial chemotaxis and diffusion across a two-dimensional surface representing...

Life Sciences, general | HIV | Mathematical and Computational Biology | Turing patterns | Mathematics | In-host viral dynamics | Chemotaxis | Reaction–diffusion | Cell Biology | Reaction-diffusion | CLEARANCE | IMMUNODEFICIENCY-VIRUS | MODEL | CD8(+) T-CELLS | THERAPY | VIRAL DYNAMICS | IN-VIVO | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | RECEPTORS | CYCLE | HIV-1 - pathogenicity | HIV Infections - virology | Humans | Mathematical Concepts | Linear Models | Male | Host-Pathogen Interactions - immunology | HIV Infections - immunology | HIV Infections - etiology | HIV-1 - immunology | Models, Biological | Computer Simulation | Female | HIV (Viruses) | Health aspects | HIV infection | Analysis

Life Sciences, general | HIV | Mathematical and Computational Biology | Turing patterns | Mathematics | In-host viral dynamics | Chemotaxis | Reaction–diffusion | Cell Biology | Reaction-diffusion | CLEARANCE | IMMUNODEFICIENCY-VIRUS | MODEL | CD8(+) T-CELLS | THERAPY | VIRAL DYNAMICS | IN-VIVO | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | RECEPTORS | CYCLE | HIV-1 - pathogenicity | HIV Infections - virology | Humans | Mathematical Concepts | Linear Models | Male | Host-Pathogen Interactions - immunology | HIV Infections - immunology | HIV Infections - etiology | HIV-1 - immunology | Models, Biological | Computer Simulation | Female | HIV (Viruses) | Health aspects | HIV infection | Analysis

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

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

There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference...

Integrablization | Discretization | Fractional differential equations | Caputo derivatives | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | RANDOM-WALKS | MULTIDISCIPLINARY SCIENCES | integrablization | MATHEMATICAL & COMPUTATIONAL BIOLOGY | discretization | MATHEMATICAL-THEORY | Approximation | Difference equations | Numerical methods | Differential equations | Order parameters | Systems analysis | Mathematical models

Integrablization | Discretization | Fractional differential equations | Caputo derivatives | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | RANDOM-WALKS | MULTIDISCIPLINARY SCIENCES | integrablization | MATHEMATICAL & COMPUTATIONAL BIOLOGY | discretization | MATHEMATICAL-THEORY | Approximation | Difference equations | Numerical methods | Differential equations | Order parameters | Systems analysis | Mathematical models

Journal Article

Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, 2016, Volume 11, Issue 3, pp. 142 - 156

There is growing evidence that many neurodegenerative disease processes involve the proliferation, accumulation and spread of pathogenic proteins. The...

Fractional diffusion | Prion disease | Anomalous transport | TIME RANDOM-WALKS | ELECTRODIFFUSION | anomalous transport | prion disease | HUMAN BRAIN | MRI | MULTIDISCIPLINARY SCIENCES | PATHOLOGY | BETA-AMYLOIDOSIS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | fractional diffusion | CABLE EQUATION MODELS | DISEASE | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DIFFUSION | TRANSMISSIBILITY | Brain | Diffusion rate | Neurodegenerative diseases | Computer simulation | Random walk | Substantia alba | Accumulation | Nodes | Neurological diseases | Proteins | Pathways | Mathematical analysis | Reaction kinetics | Mathematical models | Kinetics | Protein transport | Power law | Binding sites | Electric power distribution

Fractional diffusion | Prion disease | Anomalous transport | TIME RANDOM-WALKS | ELECTRODIFFUSION | anomalous transport | prion disease | HUMAN BRAIN | MRI | MULTIDISCIPLINARY SCIENCES | PATHOLOGY | BETA-AMYLOIDOSIS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | fractional diffusion | CABLE EQUATION MODELS | DISEASE | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DIFFUSION | TRANSMISSIBILITY | Brain | Diffusion rate | Neurodegenerative diseases | Computer simulation | Random walk | Substantia alba | Accumulation | Nodes | Neurological diseases | Proteins | Pathways | Mathematical analysis | Reaction kinetics | Mathematical models | Kinetics | Protein transport | Power law | Binding sites | Electric power distribution

Journal Article

18.
Full Text
Generalized fractional diffusion equations for subdiffusion in arbitrarily growing domains

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

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

The introduction of fractional-order derivatives to epidemiological compartment models, such as SIR models, has attracted much attention. When this...

Epidemics | Stochastic processes | Random walk | Dengue fever | Probability | Infections | Mathematics | Derivatives | Epidemiology | Recovery | Time dependence | Infectious diseases | Disease transmission | Ordinary differential equations | Mathematical models | Stochastic models | SIR models | epidemiological models | continuous-time random walk | fractional-order differential equations

Epidemics | Stochastic processes | Random walk | Dengue fever | Probability | Infections | Mathematics | Derivatives | Epidemiology | Recovery | Time dependence | Infectious diseases | Disease transmission | Ordinary differential equations | Mathematical models | Stochastic models | SIR models | epidemiological models | continuous-time random walk | fractional-order differential equations

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.