FDA Express Vol. 4, No. 5, Sep. 15, 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
◆ Latest SCI Journal Papers on FDA
◆ Books
Fractional Derivatives for Physicists and Engineers
Selected Aspects of Fractional Brownian Motion
◆ Journals
An Interdisciplinary Journal of Discontinuity, Nonlinearity, and Complexity
Journal of Applied Nonlinear Dynamics
Communications in Nonlinear Science and Numerical Simulation (Volume 18, Issue 1)
Communications in Nonlinear Science and Numerical Simulation (Volume 18, Issue 2)
◆ Classical Papers
Polynomial operators, stieltjes convolution, and fractional calculus in hereditary mechanics
Analysis of four-parameter fractional derivative model of real solid materials
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Latest
SCI Journal Papers on FDA
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1. Title:
Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries
equations
Author(s): Sahadevan, R.; Bakkyaraj, T.
Source: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: 393 Issue:
2 Pages: 341-347 DOI: 10.1016/j.jmaa.2012.04.006 Published: SEP 15 2012
2. Title: Space-time fractional diffusion on bounded domains
Author(s): Chen, Zhen-Qing; Meerschaert, Mark M.; Nane, Erkan
Source: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: 393 Issue:
2 Pages: 479-488 DOI: 10.1016/j.jmaa.2012.04.032 Published: SEP 15 2012
3. Title: CONTINUOUS-TIME FINANCE AND THE WAITING TIME DISTRIBUTION: MULTIPLE CHARACTERISTIC TIMES
Author(s): Fa, Kwok Sau
Source: MODERN PHYSICS LETTERS B Volume: 26 Issue: 23 Article Number:
1250151 DOI: 10.1142/S0217984912501515 Published: SEP 10 2012
4.
Title:
Fractional optimal control of distributed systems in spherical and cylindrical
coordinates
Author(s): Hasan, M. Mehedi; Tangpong, Xiangqing W.; Agrawal, Om Prakash
Source: JOURNAL OF VIBRATION AND CONTROL Volume: 18 Issue: 10 Pages: 1506-1525 DOI: 10.1177/1077546311408471 Published: SEP 2012
Author(s): Zhang, BiTao; Pi, YouGuo; Luo, Ying
Source: ISA TRANSACTIONS Volume: 51 Issue: 5 Pages: 649-656 DOI: 10.1016/j.isatra.2012.04.006 Published: SEP 2012
6. Title: Fractional differential inclusions with fractional separated boundary conditions
Author(s): Ahmad, Bashir; Ntouyas, Sotiris K.
Source: FRACTIONAL CALCULUS AND APPLIED ANALYSIS Volume: 15 Issue: 3 Pages:
362-382 DOI: 10.2478/s13540-012-0027-y Published: SEP 2012
7. Title: Towards a combined fractional mechanics and quantization
Author(s): Malinowska, Agnieszka B.; Torres, Delfim F. M. Source: FRACTIONAL CALCULUS AND APPLIED ANALYSIS Volume: 15 Issue: 3 Pages: 407-417 DOI: 10.2478/s13540-012-0029-9 Published: SEP 2012
Author(s): Ahmad, Bashir; Nieto, Juan J.
Source: FRACTIONAL CALCULUS AND APPLIED ANALYSIS Volume: 15 Issue: 3 Pages:
451-462 DOI: 10.2478/s13540-012-0032-1 Published: SEP 2012
Author(s): Graef, John R.; Kong, Lingju; Kong, Qingkai; et al.
Source: FRACTIONAL CALCULUS AND APPLIED ANALYSIS Volume: 15 Issue: 3 Pages:
509-528 DOI: 10.2478/s13540-012-0036-x Published: SEP 2012
10. Title: Design of analog variable fractional order differentiator and integrator
Author(s): Charef, Abdelfatah; Idiou, Daoud
Source: NONLINEAR DYNAMICS Volume: 69 Issue: 4 Pages: 1577-1588 DOI:
10.1007/s11071-012-0370-x Published: SEP 2012
Author(s): Lin, Tsung-Chih; Kuo, Chia-Hao; Lee, Tun-Yuan; et al.
Source: NONLINEAR DYNAMICS Volume: 69 Issue: 4 Pages: 1639-1650 DOI: 10.1007/s11071-012-0375-5 Published: SEP 2012
Author(s): Tusset, A. M.; Balthazar, J. M.; Bassinello, D. G.; et al.
Source: NONLINEAR DYNAMICS Volume: 69 Issue: 4 Pages: 1837-1857 DOI: 10.1007/s11071-012-0390-6 Published: SEP 2012
Author(s): Liu, Ling; Liang, Deliang; Liu, Chongxin
Source: NONLINEAR DYNAMICS Volume: 69 Issue: 4 Pages: 1929-1939 DOI: 10.1007/s11071-012-0397-z Published: SEP 2012
14. Title: Dynamics analysis and hybrid function projective synchronization of a new chaotic system
Author(s): Wu, Xiangjun; Li, Shanzhi
Source: NONLINEAR DYNAMICS Volume: 69 Issue: 4 Pages: 1979-1994 DOI: 10.1007/s11071-012-0401-7 Published: SEP 2012
Author(s): Das, Saptarshi; Pan, Indranil; Das, Shantanu; et al.
Source: NONLINEAR DYNAMICS Volume: 69 Issue: 4 Pages: 2193-2206 DOI: 10.1007/s11071-012-0419-x Published: SEP 2012
16. Title: Synchronization between fractional-order Ravinovich-Fabrikant and Lotka-Volterra systems
Author(s): Agrawal, S. K.; Srivastava, M.; Das, S.
Source: NONLINEAR DYNAMICS Volume: 69 Issue: 4 Pages: 2277-2288 DOI: 10.1007/s11071-012-0426-y Published: SEP 2012
17. Title: Analysis of differential equations of fractional order
Author(s): Sayevand, K.; Golbabai, A.; Yildirim, Ahmet
Source: APPLIED MATHEMATICAL MODELLING Volume: 36 Issue: 9 Pages: 4356-4364 DOI: 10.1016/j.apm.2011.11.061 Published: SEP 2012
18. Title: Resolvents for weakly singular kernels and fractional differential equations
Author(s): Becker, Leigh C.
Source: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS Volume: 75 Issue: 13 Pages: 4839-4861 DOI: 10.1016/j.na.2012.04.001 Published: SEP 2012
Author(s): Saha, Suman; Das, Saptarshi; Das, Shantanu; et al.
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 17 Issue: 9 Pages: 3628-3642 DOI: 10.1016/j.cnsns.2012.01.007 Published: SEP 2012
20. Title: Sensitivity analysis of CRA based controllers in fractional order systems
Author(s): Tabatabaei, Mohammad; Haeri, Mohammad
Source: SIGNAL PROCESSING Volume: 92 Issue: 9 Pages: 2040-2055 DOI: 10.1016/j.sigpro.2012.01.014 Published: SEP 2012
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Books
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Vladimir V. Uchaikin
· First book combining a clear introduction to the fractional calculus with the description of a wide sphere of physical applications
· Combined ease of access and breadth of scope
· Enables readers to apply the new methods in their own research
The first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. Fractional Derivatives for Physicists and Engineers— The first volume contains a clear introduction into such a modern branch of analysis as the fractional calculus. The second develops a wide panorama of applications of the fractional calculus to various physical problems. This book recovers new perspectives in front of the reader dealing with turbulence and semiconductors, plasma and thermodynamics, mechanics and quantum optics, nanophysics and astrophysics.
The book is addressed to students, engineers and physicists, specialists in theory of probability and statistics, in mathematical modeling and numerical simulations, to everybody who doesn't wish to stay apart from the new mathematical methods becoming more and more popular.
Prof. Vladimir V. UCHAIKIN is a known Russian scientist and pedagogue, a Honored Worker of Russian High School, a member of the Russian Academy of Natural Sciences. He is the author of about three hundreds articles and more than a dozen books (mostly in Russian) in Cosmic ray physics, Mathematical physics, Levy stable statistics, Monte Carlo methods with applications to anomalous processes in complex systems of various levels: from quantum dots to the Milky Way galaxy.
Keywords: Applications Fractional derivatives - Fractals physics - Hereditarity - Stable statistics
Related subjects: Computational Science & Engineering - Physical & Information Science - Theoretical, Mathematical & Computational Physics
Table of contents
· Physical Basics
· Fractional Derivatives
· Fractional Equations
· Applications
· Mechanics
· Kinetics
· Electrodynamics
· Atomic Physics
· Space Physics
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Ivan Nourdin
http://www.springer.com/mathematics/probability/book/978-88-470-2822-7
· Except for very few exception, every result stated in this book is proved in details: the book is then perfectly tailored for self-learning
· My guiding thread was to develop only the most aesthetic topics related to fractional Brownian motion: the book will appeal to readers who are not necessarily familiar with fractional Brownian motion and who like beautiful mathematics
· A special chapter on a recent link between fractional Brownian motion and free probability introduces the reader to a new and promising line of research
Fractional Brownian motion (fBm) is a stochastic process which deviates significantly from Brownian motion and semimartingales, and others classically used in probability theory. As a centered Gaussian process, it is characterized by the stationarity of its increments and a medium- or long-memory property which is in sharp contrast with martingales and Markov processes. FBm has become a popular choice for applications where classical processes cannot model these non-trivial properties; for instance long memory, which is also known as persistence, is of fundamental importance for financial data and in internet traffic. The mathematical theory of fBm is currently being developed vigorously by a number of stochastic analysts, in various directions, using complementary and sometimes competing tools. This book is concerned with several aspects of fBm, including the stochastic integration with respect to it, the study of its supremum and its appearance as limit of partial sums involving stationary sequences, to name but a few. The book is addressed to researchers and graduate students in probability and mathematical statistics. With very few exceptions (where precise references are given), every stated result is proved.
Content Level: Research
Keywords: Fractional Brownian motion - Integration - Limit theorems - Malliavin calculus - Maximum of Gaussian processes
Related subjects: Probability Theory and Stochastic Processes - Quantitative Finance
Table of contents
·
Preliminaries
· Fractional Brownian motion
· Integration with respect to fractional Brownian motion
· Supremum of the fractional Brownian motion
· Malliavin calculus in a nutshell
· Central limit theorem on the Wiener space
· Weak convergence of partial sums of stationary sequences
· Non-commutative fractional Brownian motion
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An Interdisciplinary Journal of Discontinuity, Nonlinearity, and Complexity
Volume 1, Number 3 September 2012
Contents
A Method for Generating Lie Algebras and Applications
Yufeng Zhang
Existence of Solutions to Weakly Generalized Vector F-implicit Variational Inequalities
Salahuddin, Ahmad M.K., R.P. Agarwal
Heat Conduction in Anisotropic Media
Nail H. Ibragimov, Elena D. Avdonina
Global Synchronization of Large Ensembles of Pulse Oscillators with Time-Delay Coupling
Vladimir V. Klinshov, Vladimir I. Nekorkin
The Dynamical Relationship Between Vegetation and Sediment in Arid and Semiarid Areas
Wei Tang, Huayong Zhang, Tousheng Huang, Liming Dai
Vectorial Inequalities for Integral Operators Involving Ratios of Functions and Convexity
George A. Anastassiou
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Journal of Applied Nonlinear Dynamics
Volume 1, Number 3 September 2012
Contents
Fluctuation Metrology Based on the Prony's Spectroscopy (II)
Raoul R. Nigmatullin
Linear Sampling Reconstructions Using a Singular Perturbation Technique
Keehwan Kim, Koung Hee Leem, George Pelekanos
Path Tracking Design by Fractional Prefilter Using a Combined QFT/H∞ Design for TDOF Uncertain Feedback Systems
N. Yousfi, P. Melchior, C. Rekik, N. Derbe, A. Oustaloup
On the Stability of a Rotating Blade with Geometric Nonlinearity
Fengxia Wang, Albert C.J. Luo
On the Fuzzy Sliding Mode Control of Nonlinear Motions in a Laminated Beam
L. Dai, L. Sun
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Communications in Nonlinear Science and Numerical Simulation
Volume 18, Issue 1
Short Communications
Articles
Letters to the Editors
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Communications in Nonlinear Science and Numerical Simulation
Volume 18, Issue 2
Review Article
Articles
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Polynomial operators, stieltjes convolution, and fractional calculus in hereditary mechanics
R.C. Koeller
Publication information: R.C. Koeller. Polynomial operators, stieltjes convolution, and fractional calculus in hereditary mechanics. ACTA MECHANICA, 58 3-4 (1986), 251-264, DOI: 10.1007/BF01176603. http://www.springerlink.com/content/lt2p66kw30680171/
Abstract
Fractional calculus is used to describe the general behavior of materials
with memory. An expression for the fractional derivative or the fractional
integral is developed in terms of the Stieltjes convolution and the Riesz
distribution. The general fractional calculus polynomial operator
constitutive equation is reduced to a Stieltjes convolution. A constitutive
equation which depends on a memory parameter for an isotorpic viscoelastic
material is presented. The proposed creep compliance has an initial
response, a primary creep region, a secondary creep region and a tertiary
creep region. The corresponding relaxation modulus has a glassy region, a
leathery region, a rubbery region and a liquid region.
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Analysis of four-parameter fractional derivative model of real solid materials
Publication information: T. Pritz. Analysis of four-parameter fractional derivative model of real solid materials. Journal of Sound and Vibration, 195(1) (1996): 103–115. http://www.sciencedirect.com/science/article/pii/S0022460X9690406X
Abstract
The introduction of fractional derivatives into the constitutive
equation of the differential operator type of linear solid materials has led
to the development of the so-called fractional derivative models. One of
these models, characterized by four parameters, has been found usable for
describing the variation of dynamics elastic and damping properties in a
wide frequency range, provided that there is only one loss peak. In this
paper this four-parameter model is theoretically analyzed. The effect of the
parameters on the frequency curves is demonstrated, and it is shown that
there is a strict relation between the dispersion of the dynamic modulus,
the loss peak and the slope of the frequency curves. The half-value
bandwidth of the loss modulus frequency curve is investigated, and
conditions are developed to establish the applicability of the model for a
class of materials. Moreover, it is shown that the model can be used to
predict the frequency dependences of dynamic properties for a wide range
even if measurements are made in only a narrow frequency range around the
loss peak.
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The End of This Issue
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