FDA Express (Vol.8, No.2, Jul.30, 2013)

Title: Approximate controllability of nonlinear fractional dynamical systems
Author(s): Sakthivel, R.; Ganesh, R.; Ren, Yong; et al.
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18 Issue: 12 Pages: 3498-3508 DOI: 10.1016/j.cnsns.2013.05.015 Published: DEC 2013

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: Initial value problems for arbitrary order fractional differential equations with delay
Author(s): Yang, Zhihui; Cao, Jinde
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18 Issue: 11 Pages: 2993-3005 DOI: 10.1016/j.cnsns.2013.03.006 Published: NOV 2013

Title: Positive solutions to singular fractional differential system with coupled boundary conditions
Author(s): Jiang, Jiqiang; Liu, Lishan; Wu, Yonghong
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18 Issue: 11 Pages: 3061-3074 DOI: 10.1016/j.cnsns.2013.04.009 Published: NOV 2013

Title: Analysis and numerical methods for fractional differential equations with delay
Author(s): Morgado, M. L.; Ford, N. J.; Lima, P. M.
Source: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 252 Pages: 159-168 DOI: 10.1016/j.cam.2012.06.034 Published: NOV 2013

Title: Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives
Author(s): Yang, Xiao-Jun; Srivastava, H. M.; He, Ji-Huan; et al.
Source: PHYSICS LETTERS A Volume: 377 Issue: 28-30 Pages: 1696-1700 DOI: 10.1016/j.physleta.2013.04.012 Published: OCT 15 2013

Title: Finite element method for Grwunwald-Letnikov time-fractional partial differential equation
Author(s): Zhang, Xindong; Liu, Juan; Wei, Leilei; et al.
Source: APPLICABLE ANALYSIS Volume: 92 Issue: 10 Pages: 2103-2114 DOI: 10.1080/00036811.2012.718332 Published: OCT 1 2013

Title: Variable-order fractional mean square displacement function with evolution of diffusibility
Author(s): Yin, Deshun; Wang, Yixin; Li, Yanqing; et al.
Source: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS Volume: 392 Issue: 19 Pages: 4571-4575 DOI: 10.1016/j.physa.2013.06.008 Published: OCT 1 2013

Title: Numerical treatment for solving the perturbed fractional PDEs using hybrid techniques
Author(s): Khader, M. M.
Source: JOURNAL OF COMPUTATIONAL PHYSICS Volume: 250 Pages: 565-573 DOI: 10.1016/j.jcp.2013.05.032 Published: OCT 1 2013

Title: Existence of solutions for impulsive differential models on half lines involving Caputo fractional derivatives
Author(s): Liu, Yuji
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18 Issue: 10 Pages: 2604-2625 DOI: 10.1016/j.cnsns.2013.02.003 Published: OCT 2013

Title: Fractional derivative and time delay damper characteristics in Duffing-van der Pol oscillators
Author(s): Leung, A. Y. T.; Guo, Zhongjin; Yang, H. X.
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18 Issue: 10 Pages: 2900-2915 DOI: 10.1016/j.cnsns.2013.02.013 Published: OCT 2013

Title: Frequency domain design of fractional order PID controller for AVR system using chaotic multi-objective optimization
Author(s): Pan, Indranil; Das, Saptarshi
Source: INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS Volume: 51 Pages: 106-118 DOI: 10.1016/j.ijepes.2013.02.021 Published: OCT 2013

Title: Dispersion curves of viscoelastic plane waves and Rayleigh surface wave in high frequency range with fractional derivatives
Author(s): Usuki, Tsuneo
Source: JOURNAL OF SOUND AND VIBRATION Volume: 332 Issue: 19 Pages: 4541-4559 DOI: 10.1016/j.jsv.2013.03.027 Published: SEP 16 2013

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Call for paper

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Call for papers: Special Issue on Analysis of Fractional Dynamic Systems

--- The Scientific World Journal

Dear Professors and Researchers,

In recent years, there has been a growing interest in dynamical systems described by fractional differential equations. This interest spans the works of many authors from various fields of science and engineering. 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. Intense work around the world is uncovering many new theoretical analysis and numerical methods for solving fractional dynamic systems. On behalf of all guest editors, I would like to invite you cordially to submit a original research articles as well as review articles in the area of fractional dynamic systems to Special Issue on Analysis of Fractional Dynamic Systems. This special issue will become an international forum for researchers to present the most recent developments and ideas in the field. The Scientific World Journal is a peer-reviewed, open access journal, meaning that all interested readers will be able to freely access the journal online without the need for a subscription. All published articles will be made available on PubMed Central and indexed in PubMed at the time of publication. Moreover, the journal currently has an Impact Factor of 1.730. Potential topics include, but are not limited to:

Mathematical models of fractional dynamical systems
Theoretical analysis of fractional dynamical systems
Numerical methods for fractional dynamical systems
Fractional image processing
Bifurcation and chaos of fractional differential systems
Fractional stochastic dynamical systems
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/tswj/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/submit/journals/ tswj/mathematical.analysis/fds/ according to the following timetable:

Manuscript Due: Friday, 10 January 2014
First Round of Reviews: Friday, 7 February 2014
Publication Date: Friday, 21 March 2014

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
RichardMagin, Department of Bioengineering, University of Illinois, 851 South Morgan Street, Chicago, IL 60607, USA; rmagin@uic.edu.
Changpin Li, Department of Mathematics, Shanghai University, Shanghai 200444, China; lcp@shu.edu.cn.
Alla Sikorskii, Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA; sikorska@stt.msu.edu.
Santos Bravo Yuste, Departmento de Física, Universidad de Extremadura, Avenida Elvas s/n, E-06071 Badajoz, Spain; santos@unex.es.

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Books

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Fractional Calculus: Theory and Applications

Varsha Daftardar-Gejji

Book Description

FRACTIONAL CALCULUS: Theory and Applications deals with differentiation and integration of arbitrary order. The origin of this subject can be traced back to the end of seventeenth century, the time when Newton and Leibniz developed foundations of differential and integral calculus. Nonetheless, utility and applicability of FC to various branches of science and engineering have been realized only in last few decades. Recent years have witnessed tremendous upsurge in research activities related to the applications of FC in modeling of real-world systems. Unlike the derivatives of integral order, the non-local nature of fractional derivatives correctly models many natural phenomena containing long memory and give more accurate description than their integer counterparts. The present book comprises of contributions from academicians and leading researchers and gives a panoramic overview of various aspects of this subject: Introduction to Fractional Calculus, Fractional Differential Equations, Fractional Ordered Dynamical Systems, Fractional Operators on Fractals, Local Fractional Derivatives, Fractional Control Systems, Fractional Operators and Statistical Distributions Applications to Engineering.

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Analysis of Variations for Self-similar Processes: A Stochastic Calculus Approach (Probability and Its Applications)

Ciprian A. Tudor

Book Description

Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged in the scientific literature. Some of them are extensions of fractional Brownian motion (bifractional Brownian motion, subtractional Brownian motion, Hermite processes), while others are solutions to the partial differential equations driven by fractional noises.

In this monograph the author discusses the basic properties of these new classes of self-similar processes and their interrelationship. At the same time a new approach (based on stochastic calculus, especially Malliavin calculus) to studying the behavior of the variations of self-similar processes has been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavin calculus.

Contents

Part I Examples of self-similar Processes

Fractional Brownian Motion and related Processes
Solutions to Linear Stochastic Heat and Wave Equation
Non-Gaussian Self-similar Processes
Multiparameter Gaussian Processes

Part II Variations of Self-similar Processes: Central and Non-Central Limit Theorems

First and Second Quadratic Variations. Wavelet-Type
Hermite Variations for Self-similar Processes

Appendix A Self-similar Processes with Self-similarity: Basic Properties
Appendix B The Kolmogorov Continuity Theorem
Appendix C Multiple Wiener Integrals and Malliavin Derivatives

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Journals

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Chaos, Solitons & Fractals

Volume 56

Collective behavior and evolutionary games – An introduction
Matjaž Perc, Paolo Grigolini

Cooperative dynamics in neuronal networks
Qingyun Wang, Yanhong Zheng, Jun Ma

Lévy flights in human behavior and cognition
Andrea Baronchelli, Filippo Radicchi

Cooperation in harsh environments and the emergence of spatial patterns
Paul E. Smaldino

The evolution of fairness in the coevolutionary ultimatum games
Kohei Miyaji, Zhen Wang, Jun Tanimoto, Aya Hagishima, Satoshi Kokubo

Does coveting the performance of neighbors of thy neighbor enhance spatial reciprocity?
Zhen Wang, Bin Wu, Ya-peng Li, Hang-xian Gao, Ming-chu Li

Quantifying the impact of noise on macroscopic organization of cooperation in spatial games
Faqi Du, Feng Fu

The effects of nonlinear imitation probability on the evolution of cooperation
Qionglin Dai, Haihong Li, Hongyan Cheng, Mei Zhang, Junzhong Yang

An evolving Stag-Hunt game with elimination and reproduction on regular lattices
Lei Wang, Chengyi Xia, Li Wang, Ying Zhang

Onset of limit cycles in population games with attractiveness driven strategy choice
Elżbieta Kukla, Tadeusz Płatkowski

Combination of continuous and binary strategies enhances network reciprocity in a spatial prisoner’s dilemma game
Noriyuki Kishimoto, Satoshi Kokubo, Jun Tanimoto

The different cooperative behaviors on a kind of scale-free networks with identical degree sequence
Yonghui Wu, Xing Li, Zhongzhi Zhang, Zhihai Rong

Effects of limited interactions between individuals on cooperation in spatial evolutionary prisoner’s dilemma game
Xu-Sheng Liu, Jian-Yue Guan, Zhi-Xi Wu

Verification and reformulation of the competitive exclusion principle
Lev V. Kalmykov, Vyacheslav L. Kalmykov

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Communications in Nonlinear Science and Numerical Simulation

Volume 18, Issue 6

Articles

Mathematical Methods

A new numerical algorithm to solve fractional differential equations based on operational matrix of generalized hat functions
Manoj P. Tripathi, Vipul K. Baranwal, Ram K. Pandey, Om P. Singh

Group classification for equations of thermodiffusion in binary mixture
Irina V. Stepanova

A composite Chebyshev finite difference method for nonlinear optimal control problems
H.R. Marzban, S.M. Hoseini

Existence and uniqueness of solutions for the nonlinear impulsive fractional differential equations
Zhenhai Liu, Xiuwen Li

Algebraic operator method for the construction of solitary solutions to nonlinear differential equations
Zenonas Navickas, Liepa Bikulciene, Maido Rahula, Minvydas Ragulskis

Direct linearization of the nonisospectral Kadomtsev–Petviashvili equation
Wei Feng, Songlin Zhao, Jianbing Zhang

The uniqueness of positive solution for a singular fractional differential system involving derivatives
Xinguang Zhang, Lishan Liu, Yonghong Wu

Nonlinear Waves and Solitons

Observation of two soliton propagation in an erbium doped inhomogeneous lossy fiber with phase modulation
M.S. Mani Rajan, A. Mahalingam, A. Uthayakumar, K. Porsezian

Chaos and Complexity

Chaotic maps-based password-authenticated key agreement using smart cards
Cheng Guo, Chin-Chen Chang

Time domain simulation of Li-ion batteries using non-integer order equivalent electrical circuit
D. Riu, M. Montaru, Y. Bultel

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Paper Highlight
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Hydraulic conductivity, velocity, and the order of the fractional dispersion derivative in a highly heterogeneous system

M.G. Herrick, D.A. Benson, M.M. Meerschaert, K.R. McCall

Publication information: M.G. Herrick, D.A. Benson, M.M. Meerschaert, K.R. McCall, Hydraulic conductivity, velocity, and the order of the fractional dispersion derivative in a highly heterogeneous system, Water Resources Research 38(11), 1227, doi:10.1029/2001WR000914.
http://onlinelibrary.wiley.com/doi/10.1029/2001WR000914/abstract

Abstract
A one-dimensional, fractional order, advection-dispersion equation accurately models the movement of the core of the tritium plume at the highly heterogeneous MADE site. An a priori estimate of the parameters in that equation, including the order of the fractional dispersion derivative, was based on the assumption that the observed power law (heavy) tail of the hydraulic conductivity (K) field would create a similarly distributed velocity field. Monte Carlo simulations were performed to test this hypothesis. Results from the Monte Carlo analysis show that heavy tailed K fields do give rise to heavy tailed velocity fields; however, the exponent of the power law (the tail parameter) describing these two distributions is not necessarily the same. The tail parameter that characterizes a velocity distribution is not solely dependent on the tail parameter that characterizes the K distribution. The K field must also have long-range dependence so that water may flow through relatively continuous high-K channels.

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Stochastic fractal-based models of heterogeneity in subsurface hydrology: Origins, applications, limitations, and future research questions

F.J. Molz, H. Rajaram, S.L. Lu

Publication information: F.J. Molz, H. Rajaram, S.L. Lu, 2004. Stochastic fractal-based models of heterogeneity in subsurface hydrology: Origins, applications, limitations, and future research questions. Review of Geophysics 42, RG1002.
http://onlinelibrary.wiley.com/doi/10.1029/2003RG000126/full

Abstract. Modern measurement techniques have shown that property distributions in natural porous and fractured media appear highly irregular and nonstationary in a spatial statistical sense. This implies that direct statistical analyses of the property distributions are not appropriate, because the statistical measures developed will be dependent on position and therefore will be nonunique. An alternative, which has been explored to an increasing degree during the past 20 years, is to consider the class of functions known as nonstationary stochastic processes with spatially stationary increments. When such increment distributions are described by probability density functions (PDFs) of the Gaussian, Levy, or gamma class or PDFs that converge to one of these classes under additions, then one is also dealing with a so-called stochastic fractal, the mathematical theory of which was developed during the first half of the last century. The scaling property associated with such fractals is called self-affinity, which is more general that geometric self-similarity. Herein we review the application of Gaussian and Levy stochastic fractals and multifractals in subsurface hydrology, mainly to porosity, hydraulic conductivity, and fracture roughness, along with the characteristics of flow and transport in such fields. Included are the development and application of fractal and multifractal concepts; a review of the measurement techniques, such as the borehole flowmeter and gas minipermeameter, that are motivating the use of fractal-based theories; the idea of a spatial weighting function associated with a measuring instrument; how fractal fields are generated; and descriptions of the topography and aperture distributions of self-affine fractures. In a somewhat different vein the last part of the review deals with fractal- and fragmentation-based descriptions of fracture networks and the implications for transport in such networks. Broad conclusions include the implication that models based on increment distributions, while more realistic, are inherently less predictive than models based directly on stationary stochastic processes; that there is presently an unresolved ambiguity when a measurement is attempted in a medium that exhibits property variations on all scales; the strong possibility that log(property) increment distributions that appear to be described by the Levy PDF are actually superpositions of several PDFs of finite variance, one for each facies; that there are apparent similarities in the transport behavior of heterogeneous porous media and fractured rock at the field scale that appear to be related to the existence of a few preferential flow paths in both types of media; and finally, that additional carefully collected data sets are needed to clarify and advance the fractal-based theories, particularly in the case of three-dimensional fracture networks where few data are available. Further refinement is needed also in the understanding of instrument spatial weighting functions in heterogeneous media and how measurements in media exhibiting variations on all scales should be interpreted.

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The End of This Issue

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