FDA Express Vol. 6, No. 6, Mar. 30, 2013
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Editors: http://em.hhu.edu.cn/fda/Editors.htm
Institute of Soft Matter Mechanics, Hohai University
For contribution: fdaexpress@163.com,
hushuaihhu@gmail.com
For subscription:
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↑ Latest SCI Journal Papers on FDA
↑ Books
Path Integrals for Stochastic Processes - An Introduction
↑ Journals
Fractional Calculus and Applied Analysis
Communications in Nonlinear Science and Numerical Simulation
↑ Paper Highlight
Applications and Implications of Fractional Dynamics for Dielectric Relaxation
Formulation of Euler每Lagrange equations for fractional variational problems
↑ Websites of Interest
Fractional Calculus & Applied Analysis, Volume 16, No 1, 2013
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Latest
SCI Journal Papers on FDA
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Title:
Development and analysis of
some versions of the fractional-order point reactor kinetics model for a nuclear
reactor with slab geometry
Author(s): Vyawahare, Vishwesh A.; Nataraj, P. S. V.
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18
Issue: 7 Pages: 1840-1856 DOI: 10.1016/j.cnsns.2012.11.012 Published: JUL 2013
Title:
A fractal Richards' equation to capture the
non-Boltzmann scaling of water transport in unsaturated media
Author(s): Sun, HongGuang; Meerschaert, Mark M.; Zhang, Yong; et al.
Source: ADVANCES IN WATER RESOURCES Volume: 52 Pages: 292-295 DOI:
10.1016/j.advwatres.2012.11.005 Published: FEB 2013
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Path Integrals for Stochastic Processes - An Introduction
Horacio S Wio
Book Description
This book provides an introductory albeit solid presentation of path integration
techniques as applied to the field of stochastic processes. The subject began
with the work of Wiener during the 1920's, corresponding to a sum over random
trajectories, anticipating by two decades Feynman's famous work on the path
integral representation of quantum mechanics. However, the true trigger for the
application of these techniques within nonequilibrium statistical mechanics and
stochastic processes was the work of Onsager and Machlup in the early 1950's.
The last quarter of the 20th century has witnessed a growing interest in this
technique and its application in several branches of research, even outside
physics (for instance, in economy).
The aim of this book is to offer a brief but complete presentation of the path
integral approach to stochastic processes. It could be used as an advanced
textbook for graduate students and even ambitious undergraduates in physics. It
describes how to apply these techniques for both Markov and non-Markov
processes. The path expansion (or semiclassical approximation) is discussed and
adapted to the stochastic context. Also, some examples of nonlinear
transformations and some applications are discussed, as well as examples of
rather unusual applications. An extensive bibliography is included. The book is
detailed enough to capture the interest of the curious reader, and complete
enough to provide a solid background to explore the research literature and
start exploiting the learned material in real situations.
Readership: Advanced undergraduate and graduate students, researchers interested
in stochastic analysis and statistical physics.
Contents:
1 Stochastic Processes: A Short Tour
2 The Path Integral for a Markov Stochastic Process
3 Generalized Path Expansion Scheme I
4 Space-Time Transform I
5 Generalized Path Expansion Scheme II
6 Space-Time Transform II
7 Non-Markov Processes: Colored Noise Case
8 Non-Markov Processes: Non-Gaussian Case
9 Non-Markov Processes: Nonlinear Case
10 Fractional Diffusion Process
11 Feynman-Kac Formula, the Influence Functional
12 Other Diffusion-Like Problems
13 What was Left Out
Appendix A Space-Time Transformation: Definitions and Solutions
Appendix B Basics Definitions in Fractional Calculus
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Volume 16, Issue 2
Fcaa Related News, Events and Books (Fcaa-Volume 16-2-2013)
Virginia Kiryakova
Fundamental solution of a distributed order time-fractional diffusion-wave
equation as probability density
Rudolf Gorenflo, Yuri Luchko, Mirjana Stojanović
Almost sure and moment stability properties of fractional order Black-Scholes
model
Caibin Zeng, YangQuan Chen, Qigui Yang
Random numbers from the tails of probability distributions using the
transformation method
Daniel Fulger, Enrico Scalas, Guido Germano
Time-fractional heat conduction in an infinite medium with a spherical hole
under robin boundary condition
Yuriy Povstenko
A note on Riesz fractional integrals in the limiting case 汐(x)p(x) √ n
Stefan Samko
Multi-parametric mittag-leffler functions and their extension
Anatoly A. Kilbas, Anna A. Koroleva, Sergei V.
Rogosin
The mellin integral transform in fractional calculus
Yuri Luchko, Virginia Kiryakova
Representation of holomorphic functions by schlömilch＊s series
Peter Rusev
The M-Wright function as a generalization of the Gaussian density for fractional
diffusion processes
Gianni Pagnini
A numerical method for the fractional Schrödinger type equation of spatial
dimension two
Neville J. Ford, M. Manuela Rodrigues, Nelson
Vieira
Fractional operators in the matrix variate case
A. M. Mathai, Hans J. Haubold
Science metrics on fractional calculus development since 1966
J. Tenreiro Machado, Alexandra M. Galhano, Juan
J. Trujillo
What Euler could further write, or the unnoticed ※big bang§ of the fractional
calculus
Igor Podlubny
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Communications in Nonlinear Science and Numerical Simulation
Volume 18, Issue 8
Local bifurcations of nonlinear viscoelastic panel in supersonic flow
Xiaohua Zhang
A wavelet method for solving a class of nonlinear boundary value problems
Xiaojing Liu, Youhe Zhou, Xiaomin Wang, Jizeng Wang
Symmetry and singularity analyses of some equations of the fifth and sixth order
in the spatial variable arising from the modelling of thin films
K. Charalambous, C. Sophocleous, P.G.L. Leach
Time-dependent MHD Couette flow in a porous annulus
Basant K. Jha, Clement A. Apere
Non-Newtonian characteristics of peristaltic flow of blood in micro-vessels
S. Maiti, J.C. Misra
Global solutions for a one-dimensional problem in conducting fluids
Jingjun Zhang, Junlei Zhu
Global solutions for nonlinear fuzzy fractional integral and integrodifferential
equations
Robab Alikhani, Fariba Bahrami
Network representation of dynamical systems: Connectivity patterns, information
and predictability
A. Garc赤a Cant迆 Ros, G. Forti, G. Nicolis
Synchronized hybrid chaotic generators: Application to real-time wireless speech
encryption
Mohamed Salah Azzaz, Camel Tanougast, Said Sadoudi, Ahmed Bouridane
Chaos control in passive walking dynamics of a compass-gait model
Hass豕ne Gritli, Nahla Khraief, Safya Belghith
An image encryption scheme using reverse 2-dimensional chaotic map and dependent
diffusion
Wei Zhang, Kwok-wo Wong, Hai Yu, Zhi-liang Zhu
Continuous-time image reconstruction for binary tomography
Yusaku Yamaguchi, Ken＊ichi Fujimoto, Omar M. Abou Al-Ola, Tetsuya Yoshinaga
Synchronous motion of two vertically excited planar elastic pendula
M. Kapitaniak, P. Perlikowski, T. Kapitaniak
Robust synchronization for stochastic delayed complex networks with switching
topology and unmodeled dynamics via adaptive control approach
Tianbo Wang, Wuneng Zhou, Shouwei Zhao
New explicit critical criterion of Hopf每Hopf bifurcation in a general discrete
time system
Huidong Xu, Guilin Wen, Qixiang Qin, Huaan Zhou
A spectral element approach for the stability analysis of time-periodic delay
equations with multiple delays
Firas A. Khasawneh, Brian P. Mann
Synchronous states in time-delay coupled periodic oscillators: A stability
criterion
Diego Paolo F. Correa, Jos谷 Roberto C. Piqueira
Numerical analysis of a population model of marine invertebrates with different
life stages
O. Angulo, J.C. L車pez-Marcos, M.A. L車pez-Marcos, J. Mart赤nez-Rodr赤guez
Pulsating traveling fronts and entire solutions in a discrete periodic system
with a quiescent stage
Hai-Qin Zhao, Shi-Liang Wu, San-Yang Liu
An observation on the periodic solutions to nonlinear physical models by means
of the auxiliary equation with a sixth-degree nonlinear term
Zehra Pınar, Turgut Öziş
Optimal estimation of parameters and states in stochastic time-varying systems
with time delay
Shahab Torkamani, Eric A. Butcher
Dynamics of hepatitis C under optimal therapy and sampling based analysis
Gaurav Pachpute, Siddhartha P. Chakrabarty
Fast-slow dynamics in Logistic models with slowly varying parameters
Jianhe Shen, Zheyan Zhou
Fundamental frequency analysis of microtubules under different boundary
conditions using differential quadrature method
M. Mallakzadeh, A.A. Pasha Zanoosi, A. Alibeigloo
Geometrically nonlinear static and dynamic analysis of functionally graded skew
plates
A.K. Upadhyay, K.K. Shukla
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Applications and Implications of Fractional Dynamics for Dielectric Relaxation
R. Hilfer
Publication information: R. Hilfer, Applications and Implications of Fractional Dynamics for Dielectric Relaxation. Recent Advances in Broadband Dielectric Spectroscopy, NATO Science for Peace and Security Series B: Physics and Biophysics 2013, pp 123-130. http://link.springer.com/chapter/10.1007/978-94-007-5012-8_9
Abstract
This article summarizes briefly the presentation given by the author at the NATO
Advanced Research Workshop on ※Broadband Dielectric Spectroscopy and its
Advanced Technological Applications§, held in Perpignan, France, in September
2011. The purpose of the invited presentation at the workshop was to review and
summarize the basic theory of fractional dynamics (Hilfer, Phys Rev E 48:2466,
1993; Hilfer and Anton, Phys Rev E Rapid Commun 51:R848, 1995; Hilfer, Fractals
3(1):211, 1995; Hilfer, Chaos Solitons Fractals 5:1475, 1995; Hilfer, Fractals
3:549, 1995; Hilfer, Physica A 221:89, 1995; Hilfer, On fractional diffusion and
its relation with continuous time random walks. In: Pekalski et al. (eds)
Anomalous diffusion: from basis to applications. Springer, Berlin, p 77, 1999;
Hilfer, Fractional evolution equations and irreversibility. In: Helbing et al. (eds)
Traffic and granular flow＊99. Springer, Berlin, p 215, 2000; Hilfer, Fractional
time evolution. In: Hilfer (ed) Applications of fractional calculus in physics.
World Scientific, Singapore, p 87, 2000; Hilfer, Remarks on fractional time. In:
Castell and Ischebeck (eds) Time, quantum and information. Springer, Berlin, p
235, 2003; Hilfer, Physica A 329:35, 2003; Hilfer, Threefold introduction to
fractional derivatives. In: Klages et al. (eds) Anomalous transport: foundations
and applications. Wiley-VCH, Weinheim, pp 17每74, 2008; Hilfer, Foundations of
fractional dynamics: a short account. In: Klafter et al. (eds) Fractional
dynamics: recent advances. World Scientific, Singapore, p 207, 2011) and
demonstrate its relevance and application to broadband dielectric spectroscopy (Hilfer,
J Phys Condens Matter 14:2297, 2002; Hilfer, Chem Phys 284:399, 2002; Hilfer,
Fractals 11:251, 2003; Hilfer et al., Fractional Calc Appl Anal 12:299, 2009).
It was argued, that broadband dielectric spectroscopy might be useful to test
effective field theories based on fractional dynamics.
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Formulation of Euler每Lagrange equations for fractional variational problems
Om P. Agrawal
Publication information: Om P. Agrawal, Formulation of Euler每Lagrange equations for fractional variational problems. Journal of Mathematical Analysis and Applications 272(1), 2002, Pages 368每379. http://www.sciencedirect.com/science/article/pii/S0022247X02001804
Abstract
This paper presents extensions to traditional calculus of variations for
systems containing fractional derivatives. The fractional derivative is
described in the Riemann每Liouville sense. Specifically, we consider two
problems, the simplest fractional variational problem and the fractional
variational problem of Lagrange. Results of the first problem are extended to
problems containing multiple fractional derivatives and unknown functions. For
the second problem, we also present a Lagrange type multiplier rule. For both
problems, we develop the Euler每Lagrange type necessary conditions which must be
satisfied for the given functional to be extremum. Two problems are considered
to demonstrate the application of the formulation. The formulation presented and
the resulting equations are very similar to those that appear in the field of
classical calculus of variations.
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