Fractional Calculus Models for the Anomalous Diffusion Processes and Their Analysis

Anomalous diffusion based on fractional calculus approach applied to drying analysis of apple slices: The effects of relative humidity and temperature

Journal of Food Process Engineering ◽

10.1111/jfpe.12549 ◽

2017 ◽

Vol 40 (5) ◽

pp. e12549 ◽

Cited By ~ 13

Author(s):

C. Ramírez ◽

V. Astorga ◽

H. Nuñez ◽

A. Jaques ◽

R. Simpson

Keyword(s):

Relative Humidity ◽

Fractional Calculus ◽

Anomalous Diffusion ◽

Apple Slices

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Fractional Calculus, Anomalous Diffusion, and Probability

Fractional Dynamics ◽

10.1142/9789814340595_0011 ◽

2011 ◽

pp. 265-284 ◽

Cited By ~ 4

Author(s):

Mark M. Meerschaert

Keyword(s):

Fractional Calculus ◽

Anomalous Diffusion

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ANOMALOUS DIFFUSION PROCESSES: STOCHASTIC MODELS AND THEIR PROPERTIES

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972720000258 ◽

2020 ◽

Vol 101 (3) ◽

pp. 514-517

Author(s):

SEAN CARNAFFAN

Keyword(s):

Anomalous Diffusion ◽

Stochastic Models ◽

Diffusion Processes

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Reaction-anomalous diffusion processes for A+B⇌C

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2019.121347 ◽

2019 ◽

Vol 527 ◽

pp. 121347 ◽

Cited By ~ 2

Author(s):

Wen-Biao Zhang ◽

Ming Yi

Keyword(s):

Anomalous Diffusion ◽

Diffusion Processes

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SCALING LAWS IN STOCHASTIC SYSTEMS WITH ANOMALOUS DIFFUSION

Fluctuation and Noise Letters ◽

10.1142/s0219477502000865 ◽

2002 ◽

Vol 02 (04) ◽

pp. L273-L278 ◽

Cited By ~ 3

Author(s):

DMITRII KHARCHENKO

Keyword(s):

Phase Space ◽

Anomalous Diffusion ◽

Stochastic System ◽

Hurst Exponent ◽

Special Class ◽

Scaling Laws ◽

Stochastic Systems ◽

Diffusion Processes ◽

Anomalous Behaviour ◽

Proposed Model

We consider the stochastic system with an anomalous diffusion. According to the obtained relations between characteristics of diffusion processes the special class of models which exhibit the anomalous behaviour is considered. It was shown that indexes of super- and subdiffusion are related to the Hürst exponent which defines the properties of the phase space inherent to the proposed model of stochastic system.

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On the self-similar, early-time, anomalous diffusion in random networks — Approach by fractional calculus

International Communications in Heat and Mass Transfer ◽

10.1016/j.icheatmasstransfer.2017.09.016 ◽

2017 ◽

Vol 89 ◽

pp. 134-138 ◽

Cited By ~ 3

Author(s):

Juan C. Padrino

Keyword(s):

Fractional Calculus ◽

Anomalous Diffusion ◽

Early Time ◽

The Self ◽

Random Networks ◽

Self Similar

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A tutorial on inverse problems for anomalous diffusion processes

Inverse Problems ◽

10.1088/0266-5611/31/3/035003 ◽

2015 ◽

Vol 31 (3) ◽

pp. 035003 ◽

Cited By ~ 74

Author(s):

Bangti Jin ◽

William Rundell

Keyword(s):

Inverse Problems ◽

Anomalous Diffusion ◽

Diffusion Processes

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FRACTIONAL DIFFUSION EQUATION, QUANTUM SUBDYNAMICS AND EINSTEIN'S THEORY OF BROWNIAN MOTION

International Journal of Modern Physics B ◽

10.1142/s0217979207045086 ◽

2007 ◽

Vol 21 (23n24) ◽

pp. 3993-3999

Author(s):

SUMIYOSHI ABE

Keyword(s):

Brownian Motion ◽

Quantum Theory ◽

Fractional Calculus ◽

Diffusion Equation ◽

Master Equation ◽

Anomalous Diffusion ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Quantum Master Equation ◽

Objective System

The fractional diffusion equation for describing the anomalous diffusion phenomenon is derived in the spirit of Einstein's 1905 theory of Brownian motion. It is shown how naturally fractional calculus appears in the theory. Then, Einstein's theory is examined in view of quantum theory. An isolated quantum system composed of the objective system and the environment is considered, and then subdynamics of the objective system is formulated. The resulting quantum master equation is found to be of the Lindblad type.

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