FDA Express Vol. 4, No. 6, Sep. 30, 2012
Editors:
W. Chen H.G. Sun
X.D. Zhang
S. Hu
Institute of Soft Matter Mechanics, Hohai University
For contribution: fdaexpress@163.com,
fdaexpress@hhu.edu.cn
For subscription:
http://em.hhu.edu.cn/fda/subscription.htm
◆ Conference
Invitation for ICF13 Session 49: Soft Matter/Materials
Fractional dynamical systems and signals
◆ Latest SCI Journal Papers on FDA
◆ Books
Introduction to the Fractional Calculus of Variations
Fractal Geometry, Complex Dimensions and Zeta Functions
◆ Journals
Fractional Calculus & Applied Analisys
International Journal of Bifurcation and Chaos (IJBC)
◆ Classical Papers
Fractional calculus and continuous-time finance II: the waiting-time distribution
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Conference
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Invitation for ICF13 Session 49: Soft Matter/Materials
The 13th International Conference on Fracture (ICF13) will be held in Beijing,
China on June 16–21, 2013. This conference is a continuation of the very
successful cosmopolitan series of quadrennial conferences.Below is its website:
http://www.icf13.org/
ICF13 is dedicated to the development and innovation in not only the traditional
and fundamental topics but also the exciting and edge-cutting arenas—from
biomedicine to geophysics, from nano/atomic to macro scales, and from physical
to holistic and system modeling.
Here I invite you to contribute an abstract to
Session 49: Soft Matter/Materials
Please noted that the deadline for abstract is the 17th October.
Many thanks for your participation and contribution. We look forward to meeting
you at the conference.
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Fractional dynamical systems and signals
-----A special session in European Control Conference 2013
http://www.ecc13.ch/
July 17-19 2013 in Zurich, Switzerland:
Special session invitation
Fractional dynamical systems and signals
Call for Papers
The goal of this
special session is to gather colleagues that work in the field of fractional
calculus in order to present the latest results in fractional dynamical systems
and signals domain. Papers describing original research work that reflects the
recent theoretical advances and experimental results as well as open new issues
for research are invited. This session will cover the following topics (but not
limited to):
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Latest
SCI Journal Papers on FDA
- Signal analysis and
filtering with fractional tools (restoration, reconstruction, analysis of
fractal noises,
- Fractional modeling
especially of (but not limited to) thermal systems, electrical systems (motors,
transformers, skin effect, …), dielectric materials, electrochemical systems
(batteries, ultracapacitors, fuel cells, …), mechanical systems (vibration
insulation, viscoelastic materials, …), Biological systems (muscles, lungs, …)
- System
identification (linear, non linear, MIMO methods, …)
- Systems
implementation (fractional controllers and filters implementation, …)
- Systems analysis
(Stability, observability, controllability, …)
- Observers
- Control (Fractional
PID, CRONE, H∞, …)
- Diagnosis of
fractional systems
Submission Deadline:
Contributed Papers and special issues must be submitted before October 19, 2012.
Submission Guidelines
Prepare our papers
according to recommendations available at
http://www.ecc13.ch/call.html
Contact if you intend to participate
Jocelyn Sabatier
IMS/LAPS: Automatique,
Productique, Signal et Image
Université Bordeaux1
- IPB -UMR 5218 CNRS
Bat A4 - 351, Cours
de la Libération
33405 Talence Cedex,
France
Email:
jocelyn.sabatier@u-bordeaux1.fr
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1. Title: Chaos and hyperchaos in fractional-order cellular neural networks
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Books
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Introduction to the Fractional Calculus of Variations
Agnieszka B Malinowska and Delfim F M Torres
http://www.worldscientific.com/worldscibooks/10.1142/p871
This invaluable book provides a broad introduction to the fascinating and beautiful subject of Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non-conservative systems in mechanics. The inclusion of non-conservatism is extremely important from the point of view of applications. Forces that do not store energy are always present in real systems. They remove energy from the systems and, as a consequence, Noether's conservation laws cease to be valid. However, it is still possible to obtain the validity of Noether's principle using FCV. The new theory provides a more realistic approach to physics, allowing us to consider non-conservative systems in a natural way. The authors prove the necessary Euler–Lagrange conditions and corresponding Noether theorems for several types of fractional variational problems, with and without constraints, using Lagrangian and Hamiltonian formalisms. Sufficient optimality conditions are also obtained under convexity, and Leitmann's direct method is discussed within the framework of FCV.
The book is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and ambitious undergraduates in mathematics and mechanics. It provides an opportunity for an introduction to FCV for experienced researchers. The explanations in the book are detailed, in order to capture the interest of the curious reader, and the book provides the necessary background material required to go further into the subject and explore the rich research literature.
Table of contents
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Fractal Geometry, Complex Dimensions and Zeta Functions
Michel L. Lapidus and Machiel van Frankenhuijsen
http://www.springer.com/mathematics/numbers/book/978-1-4614-2175-7
· The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings
· Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary
· Numerous theorems, examples, remarks and illustrations enrich the text
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings; that is, one-dimensional drums with fractal boundary. This second edition of Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, complex analysis, distribution theory, and mathematical physics. The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level.
Key Features include:
· The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings
· Complex dimensions of a fractal string are studied in detail, and used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra
· Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal
· Examples of such explicit formulas include a Prime Orbit Theorem with error term for self-similar flows, and a geometric tube formula
· The method of Diophantine approximation is used to study self-similar strings and flows
· Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions
· The unique viewpoint of this book culminates in the definition of fractality as the presence of nonreal complex dimensions. The final chapter (13) is new to the second edition and discusses several new topics, results obtained since the publication of the first edition, and suggestions for future developments in the field.
Review of the First Edition:
" The book is self contained, the material organized in chapters preceded by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actually has many applications."
—Nicolae-Adrian Secelean, Zentralblatt
Table of contents
·
Preface
·
Overview
·
Introduction
·
Complex Dimensions of
Ordinary Fractal Strings
·
Complex Dimensions of
Self-Similar Fractal Strings
·
Complex Dimensions of
Nonlattice Self-Similar Strings
· Generalized Fractal Strings Viewed as Measures
· Explicit Formulas for Generalized Fractal Strings
· The Geometry and the Spectrum of Fractal Strings
· Periodic Orbits of Self-Similar Flows
· Fractal Tube Formulas
· Riemann Hypothesis and Inverse Spectral Problems
· Generalized Cantor Strings and their Oscillations
· Critical Zero of Zeta Functions
· Fractality and Complex Dimensions
· Recent Results and Perspectives
· Appendix A. Zeta Functions in Number Theory
· Appendix B. Zeta Functions of Laplacians and Spectral Asymptotics
· Appendix C. An Application of Nevanlinna Theory
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Fractional Calculus & Applied Analisys
Vol. 15, No 4 (2012)
Editorial: FCAA RELATED MEETINGS, BOOKS, IN
MEMORIAM (FCAA - Volume 15 - No 4)
FRACTIONAL CALCULUS FOR POWER FUNCTIONS AND EIGENVALUES OF THE FRACTIONAL
LAPLACIAN
B. Duda
BERNSTEIN POLYNOMIALS FOR SOLVING FRACTIONAL HEAT- AND WAVE-LIKE EQUATIONS
D. Rostamy, K. Karimi
FUZZY FRACTIONAL INTEGRAL EQUATIONS UNDER COMPACTNESS TYPE CONDITION
R.P. Agarwal, S. Arshad, D. O'Regan, V. Lupulescu
EXISTENCE RESULTS FOR SEMILINEAR FRACTIONAL DIFFERENTIAL EQUATIONS VIA
KURATOWSKI MEASURE OF NONCOMPACTNESS
Li Kexue, Peng Jigen, Gao Jinghuai
A UNIQUENESS RESULT FOR A FRACTIONAL DIFFERENTIAL EQUATION
R.A.C. Ferreira
FRACTIONAL CALCULUS ON TIME SCALES WITH TAYLOR'S THEOREM
P.A. Williams
ON A CLASS OF TIME-FRACTIONAL DIFFERENTIAL EQUATIONS
C.-G. Li, M. Kostic, M. Li, S. Piskarev
NUMERICAL STUDIES FOR THE VARIABLE-ORDER NONLINEAR FRACTIONAL WAVE EQUATION
N.H. Sweilam, M.M. Khader, H.M. Almarwm
SOLUTION OF FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS USING ITERATIVE METHOD
C.D. Dhaigude, V.R. Nikam
SOME GENERALIZED FRACTIONAL CALCULUS OPERATORS AND THEIR APPLICATIONS IN
INTEGRAL EQUATIONS
O. Agrawal
AN HISTORICAL PERSPECTIVE ON FRACTIONAL CALCULUS IN LINEAR VISCOELASTICITY
F. Mainardi
THE DERIVATION OF THE GENERALIZED FUNCTIONAL EQUATIONS DESCRIBING SELF-SIMILAR
PROCESSES
R.R. Nigmatulllin, D. Baleanu
[Back]
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International Journal of Bifurcation and Chaos (IJBC)
in Applied Sciences and Engineering
Volume 22, Number
8
http://www.worldscientific.com/worldscinet/ijbc
Tutorials and Reviews
The Homotopy Analysis Method in Bifurcation Analysis Of Delay Differential Equations
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Volume 45, Issues 9–10
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Yuriy A. Rossikhin
and Marina V. Shitikova
Publication information:
Yuriy A. Rossikhin and Marina V. Shitikova. Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids. Appl. Mech. Rev. 1997, 50(1): 15 (53 pages).
Abstract: The aim of this review article is to collect together separated results of research in the application of fractional derivatives and other fractional operators to problems connected with vibrations and waves in solids having hereditarily elastic properties, to make critical evaluations, and thereby to help mechanical engineers who use fractional derivative models of solids in their work. Since the fractional derivatives used in the simplest viscoelastic models (Kelvin-Voigt, Maxwell, and standard linear solid) are equivalent to the weakly singular kernels of the hereditary theory of elasticity, then the papers wherein the hereditary operators with weakly singular kernels are harnessed in dynamic problems are also included in the review. Merits and demerits of the simplest fractional calculus viscoelastic models, which manifest themselves during application of such models in the problems of forced and damped vibrations of linear and nonlinear hereditarily elastic bodies, propagation of stationary and transient waves in such bodies, as well as in other dynamic problems, are demonstrated with numerous examples. As this takes place, a comparison between the results obtained and the results found for the similar problems using viscoelastic models with integer derivatives is carried out. The methods of Laplace, Fourier and other integral transforms, the approximate methods based on the perturbation technique, as well as numerical methods are used as the methods of solution of the enumerated problems.
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Fractional calculus and continuous-time finance II: the waiting-time distribution
, Marco Raberto , Rudolf Gorenflo, Enrico ScalasPublication information:
Francesco Mainardi,
Marco Raberto,
Rudolf Gorenflo,
Enrico Scalas.
Fractional calculus and continuous-time finance II: the waiting-time
distribution.
Physica A, 2000,
287(3-4):468-481.
http://www.sciencedirect.com/science/article/pii/S0378437100003861
Abstract: We complement the theory of tick-by-tick dynamics of financial markets based on a continuous-time random walk (CTRW) model recently proposed by Scalas et al. (Physica A 284 (2000) 376), and we point out its consistency with the behaviour observed in the waiting-time distribution for BUND future prices traded at LIFFE, London.
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The End of This Issue
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