FDA Express (Vol.7, No.1, Apr.15, 2013)

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

(Searched on 12 April 2013)

¡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

Chaos

Communications in Nonlinear Science and Numerical Simulation

A special issue of Philosophical Transactions of the Royal Society A on Fractional calculus and its applications

¡ô  Paper Highlight

A fractional calculus approach to the description of stress and strain localization in fractal media

Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions

¡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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(Searched on 12 April 2013)

from ISI Web of Science (SCI)

Title: A boundary value problem of fractional differential equations with anti-periodic type integral boundary conditions
Author(s): Ahmad, Bashir; Ntouyas, S. K.
Source: JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS Volume: 15 Issue: 8 Pages: 1372-1380 Published: DEC 2013

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

£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­

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

£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­

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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Books

£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­£­

Fractional Derivatives for Physicists and Engineers: Volume I Background and Theory Volume II Applications (Nonlinear Physical Science)

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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Journals

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Chaos 

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

Straight-line backbone curve
Ivana Kovacic, Richard Rand

Stability analysis of a stochastic logistic model with infinite delay
Meng Liu, Dejun Fan, Ke Wang

A description of Lax type integrable dynamical systems via the Marsden¨CWeinstein reduction method
Yarema A. Prykarpatsky

Regular Articles

Mathematical Methods

Systematic construction of infinitely many conservation laws for certain nonlinear evolution equations in mathematical physics
Xing L¨¹, Mingshu Peng

Symmetry reduction, exact solutions and conservation laws of a new fifth-order nonlinear integrable equation
Gang-wei Wang, Xi-qiang Liu, Ying-yuan Zhang

Lie symmetry analysis to the time fractional generalized fifth-order KdV equation
Gang-wei Wang, Xi-qiang Liu, Ying-yuan Zhang

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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Paper Highlight
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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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Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions

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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