FDA Express Vol. 7, No. 1, Apr. 15, 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:
http://em.hhu.edu.cn/fda/subscription.htm
PDF Download: http://em.hhu.edu.cn/fda/Issues/FDA_Express_Vol7_No1_2013.pdf
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¡ô Latest SCI Journal Papers on FDA
¡ô Conferences
Mini-Symposium on "Numerical Methods for Fractional Derivative Equations"
¡ô Call for Paper
Special Issue on Fractional Differential Equations (2013)
¡ô Books
Fractional Derivatives for Physicists and Engineers: Volume I Background and Theory Volume II Applications (Nonlinear Physical Science)¡ô Journals
Communications in Nonlinear Science and Numerical Simulation
¡ô Paper Highlight
A fractional calculus approach to the description of stress and strain localization in fractal media
¡ô 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:
Analytic Approximation of Time-Fractional
Diffusion-Wave Equation Based on Connection of Fractional and Ordinary Calculus
Author(s): Fallahgoul, H.; Hashemiparast, S. M.
Source: JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS Volume: 15 Issue: 8
Pages: 1430-1443 Published: DEC 2013
Title:
Higher order duality in nondifferentiable
fractional programming involving generalized convexity
Author(s): Ahmad, I.; Agarwal, Ravi P.; Jayswal, Anurag
Source: JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS Volume: 15 Issue: 8
Pages: 1444-1455 Published: DEC 2013
Title:
Error estimate in fractional differential
equations using multiquadratic radial basis functions
Author(s): Kazemi, B. Fakhr; Ghoreishi, F.
Source: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 245 Pages:
133-147 DOI: 10.1016/j.cam.2012.12.011 Published: JUN 2013
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Conferences
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Mini-Symposium on "Numerical Methods for Fractional Derivative Equations"
in association with "The 5th Asia Pacific Congress on Computational Mechanics &
4th International Symposium on Computational Mechanics"
---- 11-14th Dec. 2013, Singapore, www.apcom2013.org
Call for Papers
The organization committee of the international conference on fractional differentiation and its applications has just opened its website at: http://www.icfda14.dieei.unict.it/
The aims of this mini-symposium are to review the progress of diverse numerical methods for fractional derivative governing equations, to seek the exciting work being undertaken in the correlative field, and to promote advanced research, development and applications.
The mini-symposium will provide communications among researchers and practitioners who are interested in this field, introduce new researchers to the field, present original ideas, report state-of-the-art and in-progress research results, discuss future trends and challenges, establish fruitful contacts, and promote interactions between researchers in numerical fractional derivative equations and those in other cross-disciplines.
The topics of this mini-symposium cover a wide range of numerical methods for fractional partial differential equations, such as finite element, finite volume, finite difference, spectral, mesh-free, matrix, decomposition methods. In particular, we welcome the research with particular application backgrounds regarding acoustics, viscosity, dynamic systems, advection-diffusion, control, geophysics, economics, statistics, just to mention a few.
All abstract (and/or full-paper) submissions should be sent to secretariat@apcom2013.org before 30 Apr. 2013. More conference info can be found at www.apcom2013.org.
Contact organizer: Prof. Wen Chen (chenwen@hhu.edu,cn)
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Call for Paper
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Special Issue on Fractional Differential Equations (2013)
Call for Papers
In recent years, a growing number of works by many authors from various fields
of science and engineering deal with dynamical systems described by fractional
differential equations. Fractional differential equations are generalization of
ordinary differential equations to arbitrary (noninteger) order. Fractional
differential equations capture nonlocal relations in space and time with power
law memory kernels. Due to extensive applications in engineering and science,
research in fractional differential equations has become an intense around the
world.
We invite authors to present original research articles as well as review
articles in the area of fractional differential equations and their
applications. This special issue will become an international forum for
researches to present the most recent developments and ideas in the field. The
topics to be covered include, but are not limited to:
Numerical methods and numerical analysis of fractional differential equations
Mathematical models of fractional dynamic systems
Fractional image processing
Theorem of fractional differential equations
Nonlinear and stochastic fractional dynamic systems
Fractional models and their experimental verifications
Applications of fractional models
Fractional random fields
Probabilistic solutions of FDE
Fractional Dynamics and Control
Before submission authors should carefully read over the journal's Author Guidelines, which are located at http://www.hindawi.com/journals/ijde/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/submit/journal/ijde/fde13/ according to the following timetable:
Manuscript Due Friday, 5 July 5 2013
First Round of Reviews Friday, 27 September 2013
Publication Date Friday, 22 November 2013
Lead Guest Editor
Fawang Liu, School of Mathematical Sciences, Queensland University of
Technology, P.O. Box 2434, Brisbane, QLD 4001, Australia; f.liu@qut.edu.au
Guest Editors
Om P. Agrawal, Department of Mechanical Engineering and Energy Processes,
Southern Illinois University, Carbondale, IL 62901, USA; om@engr.siu.edu
Shaher Momani, Department of Mathematics, The University of Jordan,Amman 11942,
Jordan; s.momani@ju.edu.jo
Nikolai N. Leonenko, School of Mathematics, Cardiff University, Cardiff CF2 4YH,
UK; leonenkon@cardiff.ac.uk
Wen Chen, Department of Engineering Mechanics, Hohai University, Xikang Road No.
1, Nanjing 210098, Jiangsu, China;
chenwen@hhu.edu.
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Vladimir V. Uchaikin
Book Description
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.
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Volume 23, Issue 1
REGULAR ARTICLES
Chaotic dynamics of a frequency-modulated microwave oscillator with time-delayed
feedback
Hien Dao, John C. Rodgers, and Thomas E. Murphy
Controlling phase multistability in coupled period-doubling oscillators
A. V. Shabunin
Influence of chaotic synchronization on mixing in the phase space of interacting
systems
Sergey V. Astakhov, Anton Dvorak, and Vadim S. Anishchenko
Spectral coarse graining for random walks in bipartite networks
Yang Wang, An Zeng, Zengru Di, and Ying Fan
On the existence and multiplicity of one-dimensional solid particle attractors
in time-dependent Rayleigh-B¨¦nard convection
Marcello Lappa
Criticality in conserved dynamical systems: Experimental observation vs. exact
properties
Dimitrije Marković, Claudius Gros, and Andr¨¦ Schuelein
Ray chaos in an architectural acoustic semi-stadium system
Xiaojian Yu and Yu Zhang
Topological field theory of dynamical systems. II
Igor V. Ovchinnikov
The estimation of neurotransmitter release probability in feedforward neuronal
network based on adaptive synchronization
Ming Xue, Jiang Wang, Chenhui Jia, Haitao Yu, Bin Deng, Xile Wei, and Yanqiu Che
L¨¦vy noise induced switch in the gene transcriptional regulatory system
Yong Xu, Jing Feng, JuanJuan Li, and Huiqing Zhang
Chaos M-ary modulation and demodulation method based on Hamilton oscillator and
its application in communication
Yongqing Fu, Xingyuan Li, Yanan Li, Wei Yang, and Hailiang Song
Nucleation pathways on complex networks
Chuansheng Shen, Hanshuang Chen, Miaolin Ye, and Zhonghuai Hou
Characterizing chaotic dynamics from simulations of large strain behavior of a
granular material under biaxial compression
Michael Small, David M. Walker, Antoinette Tordesillas, and Chi K. Tse
Self avoiding paths routing algorithm in scale-free networks
Abdeljalil Rachadi, Mohamed Jedra, and Noureddine Zahid
Bouncing droplets on a billiard table
David Shirokoff
A unified model for the dynamics of driven ribbon with strain and magnetic order
parameters
Ritupan Sarmah and G. Ananthakrishna
Control of a model of DNA division via parametric resonance
Wang Sang Koon, Houman Owhadi, Molei Tao, and Tomohiro Yanao
Generalized variable projective synchronization of time delayed systems
Santo Banerjee, S. Jeeva Sathya Theesar, and J. Kurths
On the absence of analytic integrability of the Bianchi Class B cosmological
models
Antoni Ferragut, Jaume Llibre, and Chara Pantazi
On the geometric formulation of Hamiltonian dynamics
Eran Calderon, Lawrence Horwitz, Raz Kupferman, and Steven Shnider
Reducing the vulnerability of network by inserting modular topologies
Zhiyun Zou, Junyi Lai, and Jianzhi Gao
Nonautonomous motion study on accelerated and decelerated solitons for the
variable-coefficient Lenells-Fokas model
Xing L¨¹ and Mingshu Peng
Two-particle circular billiards versus randomly perturbed one-particle circular
billiards
Sandra Ranković and Mason A. Porter
Multi-stage complex contagions
Sergey Melnik, Jonathan A. Ward, James P. Gleeson, and Mason A. Porter
Harnessing quantum transport by transient chaos
Rui Yang, Liang Huang, Ying-Cheng Lai, Celso Grebogi, and Louis M. Pecora
On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation
K. R. Khusnutdinova, C. Klein, V. B. Matveev, and A. O. Smirnov
Topology identification of uncertain nonlinearly coupled complex networks with
delays based on anticipatory synchronization
Yanqiu Che, Ruixue Li, Chunxiao Han, Shigang Cui, Jiang Wang, Xile Wei, and Bin
Deng
Effects of time delay on the stochastic resonance in small-world neuronal
networks
Haitao Yu, Jiang Wang, Jiwei Du, Bin Deng, Xile Wei, and Chen Liu
Cross-correlation detection and analysis for California's electricity market
based on analogous multifractal analysis
Fang Wang, Gui-ping Liao, Jian-hui Li, Rui-biao Zou, and Wen Shi
Conjugate feedback induced suppression and generation of oscillations in the
Chua circuit: Experiments and simulations
Tirtha Mandal, Tanu Singla, M. Rivera, and P. Parmananda
Temporal dynamics and impact of event interactions in cyber-social populations
Yi-Qing Zhang and Xiang Li
The dynamics of hybrid metabolic-genetic oscillators
Ed Reznik, Tasso J. Kaper, and Daniel Segr¨¨
Multifractal analysis of validated wind speed time series
A. P. Garc¨ªa-Mar¨ªn, J. Est¨¦vez, F. J. Jim¨¦nez-Hornero, and J. L. Ayuso-Muñoz
Non-specular reflections in a macroscopic system with wave-particle duality:
Spiral waves in bounded media
Jacob Langham and Dwight Barkley
Hierarchical networks, power laws, and neuronal avalanches
Eric J. Friedman and Adam S. Landsberg
Effect of multiple time-delay on vibrational resonance
C. Jeevarathinam, S. Rajasekar, and M. A. F. Sanju¨¢n
Individuality of breathing patterns in patients under noninvasive mechanical
ventilation evidenced by chaotic global models
Christophe Letellier, Giovani G. Rodrigues, Jean-François Muir, and Luis A.
Aguirre
Short desynchronization episodes prevail in synchronous dynamics of human brain
rhythms
Sungwoo Ahn and Leonid L. Rubchinsky
Network-based stochastic competitive learning approach to disambiguation in
collaborative networks
Thiago Christiano Silva and Diego Raphael Amancio
Compound synchronization of four memristor chaotic oscillator systems and secure
communication
Junwei Sun, Yi Shen, Quan Yin, and Chengjie Xu
Coupling and noise induced spiking-bursting transition in a parabolic bursting
model
Lin Ji, Jia Zhang, Xiufeng Lang, and Xiuhui Zhang
Robust detection of dynamic community structure in networks
Danielle S. Bassett, Mason A. Porter, Nicholas F. Wymbs, Scott T. Grafton, Jean
M. Carlson, and Peter J. Mucha
Soliton dynamics in media with space stimulated Raman scattering and synchronic
spatial variation of dispersion and self-phase modulation
N. V. Aseeva, E. M. Gromov, and V. V. Tyutin
Tendency to occupy a statistically dominant spatial state of the flow as a
driving force for turbulent transition
Sergei F. Chekmarev
Integrated computation of finite-time Lyapunov exponent fields during direct
numerical simulation of unsteady flows
Justin Finn and Sourabh V. Apte
Spike phase synchronization in delayed-coupled neural networks:
Uniform vs. non-uniform transmission delay
Mahdi Jalili
Dust-acoustic Gardner solitons and double layers in dusty plasmas with
nonthermally distributed ions of two distinct temperatures
I. Tasnim, M. M. Masud, M. Asaduzzaman, and A. A. Mamun
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Communications in Nonlinear Science and Numerical Simulation
Volume 18, Issue 9
Short Communications
Stability analysis of a stochastic logistic model with infinite delay
A description of Lax type integrable dynamical systems via the Marsden¨CWeinstein reduction method
Regular Articles
Mathematical Methods
Lie symmetry analysis to the time fractional generalized fifth-order KdV equation
Developing an SL(2, R) Lie-group shooting method for a singular ϕ-Laplacian in a
nonlinear ODE
Chein-Shan Liu
On the second-order approximate symmetry classification and optimal systems of
subalgebras for a forced Korteweg¨Cde Vries equation
G.F. Jefferson
Symmetry analysis of a heat conduction model for heat transfer in a longitudinal
rectangular fin of a heterogeneous material
Raseelo J. Moitsheki, Bronwyn H. Bradshaw-Hajek
Some new solutions for the Derrida¨CLebowitz¨CSpeer¨CSpohn equation
J. Ram¨ªrez, J.L. Romero, R. Tracin¨¤
Nonlinear Waves and Solitons
The drift of spirals under competitive illumination in an excitable medium
Guiquan Liu, Ningjie Wu, Heping Ying
Complete classification of discrete resonant Rossby/drift wave triads on
periodic domains
Miguel D. Bustamante, Umar Hayat
Solitary wave solutions and modulation instability analysis of the nonlinear
Schrodinger equation with higher order dispersion and nonlinear terms
Manirupa Saha, Amarendra K. Sarma
Breathers and multi-soliton solutions for the higher-order generalized nonlinear
Schrödinger equation
Rui Guo, Hui-Qin Hao
Nonlinear Fluids
Chaotic convection in a ferrofluid
D. Laroze, P.G. Siddheshwar, H. Pleiner
Computational analysis of CO2 emission, O2 depletion and thermal decomposition
in a cylindrical pipe filled with reactive materials
T. Chinyoka, O.D. Makinde
Chaos and Complexity
Finite-time synchronization control of complex dynamical networks with time
delay
Jun Mei, Minghui Jiang, Wangming Xu, Bin Wang
A computational toy model for shallow landslides: Molecular dynamics approach
Gianluca Martelloni, Franco Bagnoli, Emanuele Massaro
Three-scale input¨Coutput modeling for urban economy: Carbon emission by Beijing
2007
G.Q. Chen, Shan Guo, Ling Shao, J.S. Li, Zhan-Ming Chen
Two compartmental fractional derivative model with fractional derivatives of
different order
Jovan K. Popović, Stevan Pilipović, Teodor M. Atanacković
A numerical study of energy consumption and time efficiency of sensor networks
with different structural topologies and routing methods
Fan Yan, Alan K.H. Yeung, Guanrong Chen
Nonlinear Dynamical Systems
Nonsingular decoupled terminal sliding-mode control for a class of fourth-order
nonlinear systems
Husnu Bayramoglu, Hasan Komurcugil
Nonlinear and chaos control of a micro-electro-mechanical system by using
second-order fast terminal sliding mode control
Song Zhankui, Kaibiao Sun
Hysteresis phenomena in shape memory alloys by non-isothermal Ginzburg¨CLandau
models
R.P. Dhote, M. Fabrizio, R.N.V. Melnik, J. Zu
Global dissipativity of a class of BAM neural networks with time-varying and
unbound delays
Zhengwen Tu, Liangwei Wang, Zhongwei Zha, Jigui Jian
Nonlinear Vibrations
Bifurcation analysis of periodic orbits of a non-smooth Jeffcott rotor model
Joseph P¨¢ez Ch¨¢vez, Marian Wiercigroch
New conditions for synchronization in complex networks with multiple
time-varying delays
Yan Dong, Jin-Guo Xian, Dong Han
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A special issue of Philosophical Transactions
of the Royal Society A on
Fractional calculus and its applications
Compiled and edited by Changpin Li, YangQuan Chen and J¨¹rgen Kurths
http://rsta.royalsocietypublishing.org/content/371/1990.toc
Introduction
Fractional calculus and its applications
Changpin Li, YangQuan Chen, and J¨¹rgen Kurths
Articles
Chaos synchronization in fractional differential systems
Fengrong Zhang, Guanrong Chen, Changpin Li, and J¨¹rgen Kurths
Some existence results on nonlinear fractional differential equations
Dumitru Baleanu, Shahram Rezapour, and Hakimeh Mohammadi
Equivalent system for a multiple-rational-order fractional differential system
Changpin Li, Fengrong Zhang, J¨¹rgen Kurths, and Fanhai Zeng
On reflection symmetry and its application to the Euler¨CLagrange equations in
fractional mechanics
Małgorzata Klimek
Fractional-order variational optical flow model for motion estimation
Dali Chen, Hu Sheng, YangQuan Chen, and Dingy¨¹ Xue
Modelling heat transfer in heterogeneous media using fractional calculus
Dominik Sierociuk, Andrzej Dzieli¨½ski, Grzegorz Sarwas, Ivo Petras, Igor
Podlubny, and Tomas Skovranek
Two-particle anomalous diffusion: probability density functions and self-similar
stochastic processes
Gianni Pagnini, Antonio Mura, and Francesco Mainardi
Application of the principal fractional meta-trigonometric functions for the
solution of linear commensurate-order time-invariant fractional differential
equations
C. F. Lorenzo, T. T. Hartley, and R. Malti
CRONE control system design toolbox for the control engineering community:
tutorial and case study
Patrick Lanusse, Rachid Malti, and Pierre Melchior
A semi-discrete finite element method for a class of time-fractional diffusion
equations
HongGuang Sun, Wen Chen, and K. Y. Sze
Stability and convergence of an implicit numerical method for the space and time
fractional Bloch¨CTorrey equation
Qiang Yu, Fawang Liu, Ian Turner, and Kevin Burrage
A high-speed algorithm for computation of fractional differentiation and
fractional integration
Masataka Fukunaga and Nobuyuki Shimizu
Matrix approach to discrete fractional calculus III: non-equidistant grids,
variable step length and distributed orders
Igor Podlubny, Tomas Skovranek, Blas M. Vinagre Jara, Ivo Petras, Viktor
Verbitsky, and YangQuan Chen
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A fractional calculus approach to the description of stress and strain localization in fractal media
Alberto Carpinteri, Pietro Cornetti
Publication information: Alberto Carpinteri, Pietro Cornetti, A fractional
calculus approach to the description of stress and strain localization in
fractal media, Chaos, Solitons & Fractals, 13(1), 2002, Pages 85-94.
http://www.sciencedirect.com/science/article/pii/S0960077900002381
Abstract
Evidence of fractal patterns in materials with disordered microstructure under
tensile loads is undeniable. Unfortunately fractal functions cannot be solution
of classical differential equations. Hence a new calculus must be developed to
handle fractal processes. In this paper, we use the local fractional calculus
operators recently introduced by K.M. Kolwankar [Studies of fractal structures
and processes using methods of fractional calculus. PhD thesis, University of
Pune, India, 1998]. Through these new mathematical tools we get the static and
kinematic equations that model the uniaxial tensile behavior of heterogeneous
materials. The fractional operators respect the non-integer (fractal) physical
dimensions of the quantities involved in the governing equations, while the
virtual work principle highlights the static-kinematic duality among them. The
solutions obtained from the model are fractal and yield to scaling power laws
characteristic of the nominal quantities, i.e., they reproduce the size effects
due to stress and strain localization.
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Guy Jumarie
Publication information: Guy Jumarie, Table of some basic fractional calculus
formulae derived from a modified Riemann-Liouville derivative for
non-differentiable functions. Applied Mathematics Letters, 22(3), 2009, Pages
378-385.
http://www.sciencedirect.com/science/article/pii/S0893965908001638
Abstract
In order to cope with some difficulties due to the fact that the
derivative of a constant is not zero with the commonly accepted Riemann-Liouvile
definition of fractional derivatives, one (Jumarie) has proposed recently an
alternative referred to as a modified Riemann-Liouville definition, which
directly, provides a Taylor¡¯s series of fractional order for non differentiable
functions. This fractional derivative provides a fractional calculus parallel
with the classical one, which applies to non-differentiable functions; and the
present short article summarizes the main basic formulae so obtained.
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