FDA Express Vol. 3, No. 1, Apr. 15, 2012
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Editors:
W. Chen H.G. Sun
X.D. Zhang
S. Hu
Institute of Soft Matter Mechanics, Hohai University
For contribution:
fdaexpress@hhu.edu.cn
For subscription:
http://em.hhu.edu.cn/fda/subscription.htm
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¡ô Conferences
Notice for registration and accommodation of FDA2012
¡ô Books
Topics in Fractional
Differential Equations
Functional Fractional Calculus
¡ô Journals
Fractional Calculus and Applied Analysis
Communications in Nonlinear Science and Numerical Simulation
¡ô Classical Papers
Anomalous Diffusion and Relaxation Close to Thermal Equilibrium: A Fractional
Fokker-Planck Equation Approach
A fractional derivative model to describe arterial viscoelasticity
¡ô Researchers & Groups
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Conferences
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Notice for registration and accommodation of FDA2012
By now, the Fifth IFAC symposium on Fractional Differentiation and its Application has received 322 abstracts and 243 full papers covering most research theoretical and application fields of fractional calculus. This notice is to call your attention on registration and accommodation of FDA2012.
All the participants (including conference committee members, Sino-German workshop participants, plenary and semi-plenary speakers) should send Registration Form and accommodation information to us before April 25, 2012, specifying your arrival and departure dates. The plenary speakers will stay at the Sunning Hotel and the Sino-German Workshop participants at the Nanjing Grand Hotel. If your Registration Form and accommodation information cannot be received before this date, we cannot guarantee your hotel reservation and your paper will not be included in the conference proceeding.
If you
have not sent Registration Form and accommodation information to us, please do
it as soon as possible (Emailbox:
fda12@hhu.edu.cn
and
sun.fda2012@gmail.com).
For information about Registration and accommodation information of FDA2012 see
http://em.hhu.edu.cn/fda12/Regaccom.html
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Books
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Saïd Abbas, Mouffak Benchohra, Gaston M. N'Gu¨¦r¨¦kata
http://www.springer.com/mathematics/dynamical+systems/book/978-1-4614-4035-2
Discusses the progress of fractional calculus as a tool in the study of dynamical systems
Presents solutions to the various classes of Darboux problems for hyperbolic differential equations
Addresses a wide audience of specialists including mathematicians, engineers, biologists, and physicists
During the last decade, there has been an explosion of interest in fractional dynamics as it was found to play a fundamental role in the modeling of a considerable number of phenomena; in particular the modeling of memory-dependent and complex media. Fractional calculus generalizes integrals and derivatives to non-integer orders and has emerged as an important tool for the study of dynamical systems where classical methods reveal strong limitations. This book is addressed to a wide audience of researchers working with fractional dynamics, including mathematicians, engineers, biologists, and physicists. This timely publication may also be suitable for a graduate level seminar for students studying differential equations.
Topics in Fractional Differential Equations is devoted to the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative. In this book, problems are studied using the fixed point approach, the method of upper and lower solution, and the Kuratowski measure of noncompactness. An historical introduction to fractional calculus will be of general interest to a wide range of researchers. Chapter one contains some preliminary background results. The second Chapter is devoted to fractional order partial functional differential equations. Chapter three is concerned with functional partial differential inclusions, while in the fourth chapter, we consider functional impulsive partial hyperbolic differential equations. Chapter five is concerned with impulsive partial hyperbolic functional differential inclusions. Implicit partial hyperbolic differential equations are considered in Chapter six, and finally in Chapter seven, Riemann-Liouville fractional order integral equations are considered. Each chapter concludes with a section devoted to notes and bibliographical remarks. The work is self-contained but also contains questions and directions for further research.
Keywords: Caputo Fractional derivative - Darboux problem - Riemann-Liouville Integral equations - fractional calculus - fractional differential equations - hyperbolic partial differential equation
Related subjects: Analysis - Dynamical Systems & Differential Equations
Table of contents
Preliminary Background
Partial Hyperbolic Functional Differential Equations
Partial Hyperbolic Functional Differential Inclusions
Impulsive Partial Hyperbolic Functional Differential Equations
Impulsive Partial Hyperbolic Functional Differential Inclusions
Implicit Partial Hyperbolic Functional Differential Equations
Fractional Order Riemann-Liouville Integral Equations
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Functional Fractional Calculus
Shantanu Das
http://www.springer.com/engineering/computational+intelligence+and+complexity/book/978-3-642-20544-6
Introduction to Fractional Calculus for scientists and engineers
Starting point for research in application of Fractional Calculus
Extended and completely overworked 2nd edition
When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ¡®ordinary¡¯ differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematical and geometrical explanations, but also several practical applications are given particularly for system identification, description and then efficient controls.
In the second edition of this successful book the concepts of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically. Various important new examples are presented, such as heterogeneity effects in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, or physics of random delay in computer networks . Special emphasis in this new edition is placed on the practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function. Practical results of viscoelastic experiments, fractional order control experiments, design of fractional controller and practical circuit synthesis for fractional order elements are presented in a modern approach as well.
Keywords: Applied Fractional Calculus - Differential Equation Systems - Functional Fractional Calculus - Generalized Fractional Calculs
Related subjects: Complexity - Computational Intelligence and Complexity - Computational Science & Engineering
Table of contents
Introduction to Fractional Calculus
Functions Used in Fractional Calculus
Observation of Fractional Calculus in Physical System Description
Concept of Fractional Divergence and Fractional Curl
Fractional Differintegrations Insight Concepts
Initialized Differintegrals and Generalized Calculus
Generalized Laplace Transform for Fractional Differintegrals
Application of Generalized Fractional Calculus in Electrical Circuit Analysis & Electromagnetics
Application of Generalized Fractional Calculus in Other Science and Engineering Fields
System Order Identification and Control
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Volume 15
, Issue 2
Editorial
Research Paper
Research Paper
Research Paper
Survey Paper
Research Paper
Research Paper
Research Paper
Research Paper
Research Paper
Survey Paper
Research Paper
Research Paper
Survey Paper
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Communications in Nonlinear Science and Numerical Simulation
Volume 17
, Issue 9
Symmetry reductions, exact solutions and conservation laws of a new coupled KdV
system
Conditional Lie¨CBäcklund symmetries and sign-invariants to second-order
evolution equations
Group theoretical modeling of thermal explosion with reactant consumption
The (G¡¯/G)-expansion method for the nonlinear lattice equations
Application of the Chebyshev pseudospectral method to van der Waals fluids
Relative controllability of fractional dynamical systems with delays in control
Bifurcation analysis of a viscoelastic fluid heated from below
Chaos suppression of a class of unknown uncertain chaotic systems via single
input
Bifurcation of travelling wave solutions for the generalized KP-MEW equations
Kolmogorov ¦Å-entropy of attractor for a non-autonomous strongly damped wave equation
Effect of noise on the reinjection probability density in intermittency
On the invariants of two dimensional linear parabolic equations
Agent-behaviour and network influence on energy innovation diffusion
Analysis of the permanence of an SIR epidemic model with logistic process and distributed time delay
Adaptive synchronization for stochastic competitive neural networks with mixed time-varying delays
Equilibrium selection under evolutionary game dynamics with optimizing behavior
Nonautonomous dynamics of coupled van der Pol oscillators in the regime of amplitude death
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Ralf Metzler, Eli Barkai, and Joseph Klafter
Publication information: R. Metzler, E. Barkai, and J. Klafter: Anomalous Diffusion and Relaxation Close to Thermal Equilibrium. Phys. Rev. Lett. 82(1999), 3563-3567. http://prl.aps.org/abstract/PRL/v82/i18/p3563_1.
We introduce a fractional Fokker-Planck equation describing the stochastic evolution of a particle under the combined influence of an external, nonlinear force and a thermal heat bath. For the force-free case, a subdiffusive behavior is recovered. The equation is shown to obey generalized Einstein relations, and its stationary solution is the Boltzmann distribution. The relaxation of single modes is shown to follow a Mittag-Leffler decay. We discuss the example of a particle in a harmonic potential.
Damian Craiem and Ricardo L. Armentano
(Contributed by Dr. ir. Clara M. IONESCU)
Publication information: D. Craiem and R. L. Armentano. A fractional derivative model to describe arterial viscoelasticity. Biorheology 44 (2007) 251¨C263. http://iospress.metapress.com/content/h4788364313648j6/
Arterial viscoelasticity can be described with a complex modulus (E*) in the frequency domain. In arteries, E* presents a power-law response with a plateau for higher frequencies. Constitutive models based on a combination of purely elastic and viscous elements can be represented with integer order differential equations but show several limitations. Recently, fractional derivative models with fewer parameters have proven to be efficient in describing rheological tissues. A new element, called ¡°spring-pot¡±, that interpolates between springs and dashpots is incorporated. Starting with a Voigt model, we proposed two fractional alternative models with one and two spring-pots. The three models were tested in an anesthetized sheep in a control state and during smooth muscle activation. A least squares method was used to fit E*. Local activation induced a vascular constriction with no pressure changes. The E* results confirmed the steep increase from static to dynamic values and a plateau in the range 2¨C30 Hz, coherent with fractional model predictions. Activation increased E*, affecting its real and imaginary parts separately. Only the model with two spring-pots correctly followed this behavior with the best performance in terms of least squares errors. In a context where activation separately modifies E*, this alternative model should be considered in describing arterial viscoelasticity in vivo.
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SCHOOL OF
CHEMISTRY, TEL AVIV UNIVERSITY
Email: klafter@post.tau.ac.il
(from http://www.tau.ac.il/~klafter1/)
Brief Biography:
BSc. Physics, Bar Ilan University (1967); MSc. Physics Bar Ilan University
(1969);
PhD. Chemistry Tel Aviv University (1978); Postdoctoral Fellow, Chemistry MIT
(1978-1980);
Exxon Research and Engineering (1980-1987); Tel Aviv University from 1987;
Chair Professor of Chemistry from 1998. Heinemann Professor of Physical
Chemistry.
Fellow American Physical Society (1993);
Alexander von Humboldt Foundation Prize (1996);
Weizmann Prize for Sciences(1999);
Kolthoff award of the Technion (2003);
Rothschild Prize in Chemistry (2004);
Israel Chemical Society Prize (2005);
Representative at the European Science Foundation, PESC committee (from 2001).
Head of Exact Sciences and Technology, Israel Science Foundation (1996-2002).
Chairman of the Academic Board of the Israel Science Foundation, ISF, (from
2002).
Fellow of the Institute for Advanced Studies (FRIAS), Freiburg
¡¡
Research Interests
Levy flights and walks and anomalous diffusion in complex systems: The concept of Levy walks, introduced by us, generalizes the known Brownian motion to include anomalous diffusion. Properties of these stochastic processes and applications to nonlinear system are investigated. Theoretical frameworks for both enhanced diffusion and subdiffusion are introduced.
Fractional Fokker-Planck equations: Since anomalous diffusion and non-exponential relaxation are already established in a broad spectrum of complex systems, modifications of the traditional kinetic equations are needed. we propose such modifications in terms of fractional calculus, and study the properties of the resulting fractional equations.
Dendrimers as light harvesting antenna systems: Energy transfer and reaction mechanisms in supermolecules such as dendrimers are investigated, following our suggestion to use these tree-like molecules for light harvesting.
Escape through fluctuating bottlenecks and resonant activation: Chemical reactions, which are described in terms of crossing fluctuating barriers are studied by mapping on random walks in finite systems.
Atomic scale friction in sheared confined systems: The "textbook" concepts of friction are being revisited in the light of the recent experimental results. Methods for controlling friction using mechanical and chemical approaches are introduced.
Molecular Engines - Car and Wheels: We have introduced a new approach to build microscopic engines on the stomic scale that move translationally or rotationally and can preform useful functions such as pulling as of a cargo. Characteristic of these engines is the possibility to determine dynamically the directionality of the motion. The approach is based on the transformation of the fed energy to directed motion through a dynamical competition between the intrinsic lenghts of the moving object and the supporting carrier.
Single
Molecules Processes: Single molecule spectroscopy is by now an
established approach, which can report on distributions of molecular
properties such as spectral diffusion, and can provide kinetic information
on conformational changes such as folding and unfolding of molecules without
the scrambling that occurs due to ensemble averaging. This information can
be valuable in particular for biomolecules, where rare events might have
functional significant, but which can be masked in an ensemble approach.
Both low temperature spectral diffusion and force measurements of single
molecules are investigated and related to experimental observations.
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Selected Papers
I. Eliazar and J. Klafter, Statistical resilience of random populations to random perturbations, Phys. Rev. E, 79, no. 011103 (2009)
M. Magdziarz, A. Weron and J. Klafter, Equivalence of the fractional Fokker-Planck and subordinated Langevin equations: The case of time-dependent force, Phys. Rev. Lett., 101, 210601 (2008)
I. Eliazar and J. Klafter, Fractal poisson processes, Physica A, 387,4985-4996 (2008)
S. B. Yuste, G. Oshanin, K. Lindenberg, O. Benichou and J. Klafter, Survival probability of a particle in a sea of mobile traps: A tale of tails, Phys. Rev. E, 78, 2, no. 021105, part 1 (2008)
A. Lubelski, I. M. Sokolov and J. Klafter, Nonergodicity inhomogeneity in single particle tracking, Phys. Rev. Lett., 100, 250602(4) (2008)
A. Lubelski and J. Klafter, Temporal correlation functions of concentration fluctuations: An anomalous case, J. Phys. Chem. B, 112, 12740-12747 (2008)
I. Eliazar and J. Klafter, Fractal probability laws, Phys. Rev. E, 77, no. 061125 (2008)
S. Reuveni, R. Granek and J. Klafter, Solutions for continuous time random walks on finite chains, Phys. Rev. Lett. 100, 20, 208101 (2008)
S. Condamin, O. Benichou, V. Tejedor, R. Voituriez and J. Klafter, First-Passage times in complex scale-invariant media, Nature 450, 77-80 (2007)
T. Koren, M.A. Lomholt, A.V. Chechkin, J. Klafter and R. Metzler, Leapover lengths and first passage time statistics for levy flights, Phys. Rev. Lett. 99, 160602 (2007)
M. A. Lomholt, M. Urbakh, R. Metzler and J. Klafter, Manipulating Single Enzymes by an External Harmonic Force, Phys. Rev. Lett. 98, 168302 (2007)
I. M. Sokolov and J. Klafter, Field-induced dispersion in subdiffusion, Phys. Rev. Lett. 97, 140602 (2006).
R. Granek and J. Klafter, Fractons in Proteins: Can they Lead to Anomalously Decaying Time Autocorrelations, Phys. Rev. Lett. 95, 098106 (2005).
O. Flomenbom, K. Velonia, D. Loos, S. Masuo, M. Cotlet, Y. Engelborghs, Hofkens, A.E. Rowan, R.J.M. Nolte, F.C. de Schryver and J. Klafter, Stretched Exponential Decay and Correlations in the Catalytic behavior of Fluctuating Individual Lipase Molecules, Proc. Nat. Acad. Sci. (USA), 102, 2368-2372 (2005).
J. Klafter and I. M. Sokolov,
Anomalous Diffusion Spreads its Wings, Physics World 18, 29-32 (2005).
¡¡
Editorial Boards
International Journal of Modern Physics B
Israel Journal of Chemistry
Journal of Physical Chemistry (1994-1999)
Journal of Luminescence
Recent
Research Developments in Physical Chemistry
¡¡
Selected Books
Co Editor of a Special Issue of J. Phys. C on ¡°Molecular Motors and Friction¡± (2005)
Co Editor of a Special Issue of Chemical Physics on "Strange Kinetics" (Nov 2002)
Co Editor of a Special Issue of Chemical Physics on ¡°Transport Properties in Disordered Systems¡± 1993
Guest Co Editor of a Special Issue of Chemical Physics in ¡°Energy Transfer and Relaxation in Low Dimensional Systems¡± (October, 1990)
Co Editor of the book ¡°Transport and Relaxation in Random Materials¡± (World Scientific, Singapore, 1987).
URL: http://www.tau.ac.il/~klafter1/
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