FDA Express Vol. 5, No. 3, Nov. 15, 2012
Editors:
W. Chen H.G. Sun
H. Wei
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
◆ Latest SCI Journal Papers on FDA
◆ Conferences
International Conference on Fractional Signals and Systems
9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)
◆ Call for Paper
Special Issue: FRACTIONAL-ORDER CIRCUITS AND SYSTEMS
◆ Books
Chaos and Fractals: An Elementary Introduction
◆ Journals
Communications in
Nonlinear Science and Numerical Simulation
Chaos, Solitons & Fractals
Journal of Computational Physics
◆ Classical Papers
Numerical comparison of methods for solving linear differential equations of
fractional order
Stability analysis of linear fractional differential system with multiple time
delays
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Latest
SCI Journal Papers on FDA
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Title:
Some generalized fractional calculus operators and their applications in
integral equations
Author(s):
Agrawal, Om P.
Source:
FRACTIONAL CALCULUS AND
APPLIED ANALYSIS Volume:
15 Issue:
4
Pages:
700-711 DOI:
10.2478/s13540-012-0047-7 Published:
DEC 2012
Title:
An historical perspective on fractional calculus in linear viscoelasticity
Author(s):
Mainardi, Francesco
Source:
FRACTIONAL CALCULUS AND
APPLIED ANALYSIS Volume:
15 Issue:
4
Pages:
712-717 DOI:
10.2478/s13540-012-0048-6 Published:
DEC 2012
Title:
The derivation of the generalized functional equations describing self-similar
processes
Author(s):
Nigmatullin, Raoul R.;
Baleanu, Dumitru
Source:
FRACTIONAL CALCULUS AND
APPLIED ANALYSIS Volume:
15 Issue:
4
Pages:
718-740 DOI:
10.2478/s13540-012-0049-5 Published:
DEC 2012
Title:
Relationships between power-law long-range interactions and fractional mechanics
Author(s):
Ishiwata, Ryosuke;
Sugiyama, Yuki
Source:
PHYSICA A-STATISTICAL
MECHANICS AND ITS APPLICATIONS Volume:
391 Issue:
23
Pages:
5827-5838 DOI:
10.1016/j.physa.2012.06.055 Published:
DEC 1 2012
Title:
Application of Avery-Peterson fixed point theorem to nonlinear boundary value
problem of fractional differential equation with the Caputo's derivative
Author(s):
Liu, Yang
Source:
COMMUNICATIONS IN
NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume:
17 Issue:
12
Pages:
4576-4584 DOI:
10.1016/j.cnsns.2012.04.010 Published:
DEC 2012
Title:
Robust synchronization of fractional-order complex dynamical networks with
parametric uncertainties
Author(s):
Wong, W. K.; Li, Hongjie;
Leung, S. Y. S.
Source:
COMMUNICATIONS IN
NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume:
17 Issue:
12
Pages:
4877-4890 DOI:
10.1016/j.cnsns.2012.05.020 Published:
DEC 2012
Title:
Non-negative solutions of systems of ODEs with coupled boundary conditions
Author(s):
Infante, Gennaro; Minhos,
Feliz M.; Pietramala, Paolamaria
Source:
COMMUNICATIONS IN
NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume:
17 Issue:
12
Pages:
4952-4960 DOI:
10.1016/j.cnsns.2012.05.025 Published:
DEC 2012
Title:
The existence of solutions for boundary value problem of fractional hybrid
differential equations
Author(s):
Sun, Shurong; Zhao, Yige;
Han, Zhenlai; et al.
Source:
COMMUNICATIONS IN
NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume:
17 Issue:
12
Pages:
4961-4967 DOI:
10.1016/j.cnsns.2012.06.001 Published:
DEC 2012
Title:
Fractional calculus modelling for unsteady unidirectional flow of incompressible
fluids with time-dependent viscosity
Author(s):
Garra, Roberto; Polito,
Federico
Source:
COMMUNICATIONS IN
NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume:
17 Issue:
12
Pages:
5073-5078 DOI:
10.1016/j.cnsns.2012.04.024 Published:
DEC 2012
Title:
Semilinear fractional differential equations based on a new integral operator
approach
Author(s):
Ding, Xiao-Li; Jiang,
Yao-Lin
Source:
COMMUNICATIONS IN
NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume:
17 Issue:
12
Pages:
5143-5150 DOI:
10.1016/j.cnsns.2012.03.036 Published:
DEC 2012
Title:
Parameter estimation and topology identification of uncertain fractional order
complex networks
Author(s):
Si, Gangquan; Sun,
Zhiyong; Zhang, Hongying; et al.
Source:
COMMUNICATIONS IN
NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume:
17 Issue:
12
Pages:
5158-5171 DOI:
10.1016/j.cnsns.2012.05.005 Published:
DEC 2012
Title:
Analytical proof on the existence of chaos in a generalized Duffing-type
oscillator with fractional-order deflection
Author(s):
Li, Huaqing; Liao,
Xiaofeng; Ullah, Saleem; et al.
Source:
NONLINEAR ANALYSIS-REAL
WORLD APPLICATIONS Volume:
13 Issue:
6
Pages:
2724-2733 DOI:
10.1016/j.nonrwa.2011.12.028 Published:
DEC 2012
Title:
Adaptive pinning synchronization in fractional-order complex dynamical networks
Author(s):
Chai, Yi; Chen, Liping;
Wu, Ranchao; et al.
Source:
PHYSICA A-STATISTICAL
MECHANICS AND ITS APPLICATIONS Volume:
391 Issue:
22
Pages:
5746-5758 DOI:
10.1016/j.physa.2012.06.050 Published:
NOV 15 2012
Title:
An efficient method for segmentation of images based on fractional calculus and
natural selection
Author(s):
Ghamisi, Pedram;
Couceiro, Micael S.; Benediktsson, Jon Atli; et al.
Source:
EXPERT SYSTEMS WITH
APPLICATIONS Volume:
39 Issue:
16
Pages:
12407-12417 DOI:
10.1016/j.eswa.2012.04.078 Published:
NOV 15 2012
Title:
The first integral method for some time fractional differential equations
Author(s):
Lu, Bin
Source:
JOURNAL OF MATHEMATICAL
ANALYSIS AND APPLICATIONS Volume:
395 Issue:
2
Pages:
684-693 DOI:
10.1016/j.jmaa.2012.05.066 Published:
NOV 15 2012
Title:
Moving boundary problems governed by anomalous diffusion
Author(s):
Vogl, Christopher J.;
Miksis, Michael J.; Davis, Stephen H.
Source:
PROCEEDINGS OF THE ROYAL
SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Volume:
468
Issue:
2147 Pages:
3348-3369
DOI:
10.1098/rspa.2012.0170 Published:
NOV 8 2012
Title:
Approximate solution to the time-space fractional cubic nonlinear Schrodinger
equation
Author(s):
Herzallah, Mohamed A.
E.; Gepreel, Khaled A.
Source:
APPLIED MATHEMATICAL
MODELLING Volume:
36 Issue:
11
Pages:
5678-5685 DOI:
10.1016/j.apm.2012.01.012 Published:
NOV 2012
Title:
An anti-periodic boundary value problem for the fractional differential equation
with a p-Laplacian operator
Author(s):
Chen, Taiyong; Liu,
Wenbin
Source:
APPLIED MATHEMATICS
LETTERS Volume:
25 Issue:
11
Pages:
1671-1675 DOI:
10.1016/j.aml.2012.01.035 Published:
NOV 2012
Title:
Parameter estimation and topology identification of uncertain fractional order
complex networks
Author(s): Si, Gangquan;
Sun, Zhiyong; Zhang, Hongying; et al.
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 17
Issue: 12 Pages: 5158-5171 DOI: 10.1016/j.cnsns.2012.05.005 Published:
DEC 2012
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Conferences
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
International Conference on Fractional Signals and Systems
7-8 November 2013
Ghent University, Ghent, Belgium
Scope
The organizing committee has the pleasure of inviting you to participate at the International Conference on Fractional Signals and Systems, FSS 2013. In 2013 the FSS will be hosted by the Ghent University, Belgium, during 7-9 November 2013.
FSS 2013 will be held at the University Conference Centre "Het Pand", in Ghent, Belgium. We sincerely welcome our colleagues worldwide to join us for FSS 2013. The conference location, Het Pand, is a historical monument: this unique building is a former Dominican Monastery, situated beside the river Leie in the historic hearth of the city of Ghent.
The history of Ghent begins in the year 630, when St Amandus chose the site of the confluence (or ‘Ganda’) of the two rivers, the Lys and the Scheldt, to construct an abbey. Nearly 1400 years of history are still palpable in the city today: a medieval castle surrounded by a moat, an imposing cathedral, a belfry, three beguinages...
Topics
• Signal analysis and filtering with fractional tools (restoration, reconstruction, analysis of fractal noises, etc.)
• Fractional modeling of thermal systems, electrical systems (motors, transformers, skin effect, etc.), dielectric materials, electrochemical systems (batteries, ultracapacitors, fuel cells, etc.), mechanical systems (vibration insulation, viscoelastic materials, etc.), biological systems (muscles, lungs, etc.) etc.
• Fractional system identification (linear, nonlinear, multivariable methods, etc.)
• Implementation aspects (fractional controllers etc.)
• Fractal structures, porous materials, etc.
Important deadlines
Submission opens: 15 April 2013
Initial submission: 1 June 2013
Author notification: 15 August 2013
Final submission: 30 September 2013
Conference dates: 7-8 November 2013
Submission Guidelines
Prepare the papers according to recommendation available at: http://www.fss13.ugent.be
Fees and registration
Until 30.09.2013 From 1.10.2013
Regular fee: 350 Eur 450 Eur
Accompanying person 180 Eur 200 Eur
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9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)
CALL FOR PAPERS
To be held in conjunction with the ASME 2013 International Design Engineering Technical Conferences at the Oregon Convention Center in Portland, Oregon, USA, August 4 - 7, 2013
(Contributed by Prof. Tenreiro Machado)
The International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC) is a premier meeting event for professional networking and research exchange across the multibody systems and nonlinear dynamics technical community. The conference facilitates the dissemination of fundamental research in the enabling disciplines as well as research into their application to engineered or naturally occurring mechanical systems across all length and time scales.
2. MSNDC- Analytical, Experimental, and Nonlinear Dynamics
• Nonlinear Resonances, Phenomena, and Interactions (B. Balachandran, S. Lenci)
• Time-Varying and Time-Delay Systems (E. Butcher, G. Oroz, S. Sinha, M. Younis)
• Reduced-Order Modeling (M. Allen, G. Kerschen, M. Eriten)
• Fractional Dynamics and Discontinuities (A. Luo, T. Machado)
Conference website: http://www.asmeconferences.org/idetc2013/
==========================================================================
Call for Paper
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IEEE Journal on Emerging and Selected Topics in Circuits and Systems
Special Issue: FRACTIONAL-ORDER CIRCUITS AND SYSTEMS
Fractional-order circuits and system design is an emerging field incorporating concepts from fractional calculus into electrical circuits and systems; showing diverse applications and immense potential in control systems, signal processing, biomedical instrumentation, and many more. As far as circuit design is concerned, there is a tremendous need to continue to generalize circuit design and analysis techniques from the narrow integer-order subset to the more general fractional-order domain and explore the unique properties of these circuits and systems.
The aim of this special issue is to expand on the analysis and design of circuits and systems approached from a fractional-order perspective. Original research papers are solicited, but not restricted to, the following areas:
• Circuit Theory of fractional-order systems
• Systematic design and realization processes of fractional-order circuits
• Analog and Digital approximation techniques of fractional systems
• Fractional-order modeling and applications (e.g. in biochemistry, biomedicine, and hybrid power systems)
• CAD tools and algorithms for simulations of fractional-order circuits
• Signal Processing based on fractional-order models
• System/sub-system level applications
Authors are invited to submit to JETCAS via the JETCAS website and according to JETCAS policies and procedures. For details see
http://jetcas.polito.it/index.html.
Timeline:
Paper submission - February 15th, 2013
First round of reviews completed - April 15th, 2013
Revised manuscripts due - May 15th, 2013
Notification of acceptance - June 1st, 2013
Final manuscripts due date - July 1st, 2013
Guest Editors:
A. S. Elwakil, elwakil@ieee.org B. Maundy, bmaundy@ucalgary.ca
G. Chen, eegchen@cityu.edu.hk L. Fortuna, lfortuna@diees.unict.it
==========================================================================
Books
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http://ukcatalogue.oup.com/product/9780199566433.do#.UJsPpEQ38xE
The only textbook on chaos and fractals for non-science and mathematics majors.
Covers central phenomena and ideas of chaos and fractals in a careful, intellectually honest, but accessible way.
Covers current areas of physics and mathematics that are of wide interest
Richly illustrated.
Over 200 end-of-chapter exercises make it easy for instructors to assign homework problems.
A range of additional topics are covered from which instructors can chose as they put together their own courses.
This book provides the reader with an elementary introduction to chaos and
fractals, suitable for students with a background in elementary algebra, without
assuming prior coursework in calculus or physics. It introduces the key
phenomena of chaos - aperiodicity, sensitive dependence on initial conditions,
bifurcations - via simple iterated functions. Fractals are introduced as
self-similar geometric objects and analyzed with the self-similarity and
box-counting dimensions. After a brief discussion of power laws, subsequent
chapters explore Julia Sets and the Mandelbrot Set. The last part of the book
examines two-dimensional dynamical systems, strange attractors, cellular
automata, and chaotic differential equations.
The book is richly illustrated and includes over 200 end-of-chapter exercises. A
flexible format and a clear and succinct writing style make it a good choice for
introductory courses in chaos and fractals.
Readership: Undergraduate students and lecturers on specialist and non-specialist courses in physics and mathematics.
Table of contents
I. Introducing Discrete Dynamical Systems
0: Opening Remarks
1: Functions
2: Iterating Functions
3: Qualitative Dynamics
4: Time Series Plots
5: Graphical Iteration
6: Iterating Linear Functions
7: Population Models
8: Newton, Laplace, and Determinism
II. Chaos
9: Chaos and the Logistic Equation
10: The Buttery Effect
11: The Bifurcation Diagram
12: Universality
13: Statistical Stability of Chaos
14: Determinism, Randomness, and Nonlinearity
III. Fractals
15: Introducing Fractals
16: Dimensions
17: Random Fractals
18: The Box-Counting Dimension
19: When do Averages exist?
20: Power Laws and Long Tails
20: Introducing Julia Sets
21: Infinities, Big and Small
IV. Julia Sets and The Mandelbrot Set
22: Introducing Julia Sets
23: Complex Numbers
24: Julia Sets for f(z) = z2 + c
25: The Mandelbrot Set
V. Higher-Dimensional Systems
26: Two-Dimensional Discrete Dynamical Systems
27: Cellular Automata
28: Introduction to Differential Equations
29: One-Dimensional Differential Equations
30: Two-Dimensional Differential Equations
31: Chaotic Differential Equations and Strange Attractors
VI. Conclusion
32: Conclusion
VII. Appendices
A: Review of Selected Topics from Algebra
B: Histograms and Distributions
C: Suggestions for Further Reading
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http://www.randomhouse.com/book/106843/the-fractalist-by-benoit-mandelbrot
A fascinating memoir
from the man who revitalized visual geometry, and whose ideas about fractals
have changed how we look at both the natural world and the financial world.
Benoit Mandelbrot, the creator of fractal geometry, has significantly improved
our understanding of, among other things, financial variability and erratic
physical phenomena. In The Fractalist, Mandelbrot recounts the high points of
his life with exuberance and an eloquent fluency, deepening our understanding of
the evolution of his extraordinary mind. We begin with his early years: born in
Warsaw in 1924 to a Lithuanian Jewish family, Mandelbrot moved with his family
to Paris in the 1930s, where he was mentored by an eminent mathematician uncle.
During World War II, as he stayed barely one step ahead of the Nazis until
France was liberated, he studied geometry on his own and dreamed of using it to
solve fresh, real-world problems. We observe his unusually broad education in
Europe, and later at Caltech, Princeton, and MIT. We learn about his
thirty-five-year affiliation with IBM’s Thomas J. Watson Research Center and his
association with Harvard and Yale. An outsider to mainstream scientific
research, he managed to do what others had thought impossible: develop a new
geometry that combines revelatory beauty with a radical way of unfolding
formerly hidden laws governing utter roughness, turbulence, and chaos.
Here is a remarkable story of both the man’s life and his unparalleled contributions to science, mathematics, and the arts.
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Communications in Nonlinear Science and Numerical Simulation
Volume 18, Issue 3
Mathematical Method
Convergence of a parameter switching algorithm for a class of nonlinear
continuous systems and a generalization of Parrondo’s paradox
Marius-F. Danca
Nonlinear Dynamical Systems
Letters to the editors
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Volume 45, Issue 12
Spatial distributions of islands in fractal surfaces and natural surfaces
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Journal of Computational Physics
Volume 232, Issue 1
Short Notes
Regular Papers
========================================================================
Numerical comparison of methods for solving linear differential equations of fractional order
S. Momani, Ζ.Μ. Odibat
Publication information: S. Momani, Ζ.Μ. Odibat. Numerical comparison of methods for solving linear differential equations of fractional order. Chaos, Solitons & Fractals 31(5) 2007, 1248-1255.
http://www.sciencedirect.com/science/article/pii/S0960077905010374
Abstract
In this article, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear differential equations of fractional order. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. This paper will present a numerical comparison between the two methods and a conventional method such as the fractional difference method for solving linear differential equations of fractional order. The numerical results demonstrates that the new methods are quite accurate and readily implemented.
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Stability analysis of linear fractional differential system with multiple time delays
Weihua Deng, Changpin Li and Jinhu Lü
Publication information: Weihua Deng, Changpin Li and Jinhu Lü. Stability analysis of linear fractional differential system with multiple time delays. NONLINEAR DYNAMICS 48(4) (2007), 409-416, DOI: 10.1007/s11071-006-9094-0.
http://www.springerlink.com/content/hm337662850tl448/
Abstract
In this paper, we study the stability of n-dimensional linear fractional differential equation with time delays, where the delay matrix is defined in (R+) n×n. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. As its an application, we apply our theorem to the delayed system in one spatial dimension studied by Chen and Moore [Nonlinear Dynamics 29, 2002, 191] and determine the asymptotically stable region of the system. We also deal with synchronization between the coupled Duffing oscillators with time delays by the linear feedback control.==========================================================================
The End of This Issue
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