FDA Express (Vol.7, No.2, Apr.30, 2013)

Title: Nonlinear fractional integro-differential equations on unbounded domains in a Banach space
Author(s): Zhang, Lihong; Ahmad, Bashir; Wang, Guotao; et al.
Source: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 249 Pages: 51-56 DOI: 10.1016/j.cam.2013.02.010 Published: SEP 2013

Title: Numerical analysis of a two-parameter fractional telegraph equation
Author(s): Ford, Neville J.; Manuela Rodrigues, M.; Xiao, Jingyu; et al.
Source: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 249 Pages: 95-106 DOI: 10.1016/j.cam.2013.02.009 Published: SEP 2013

Title: Lie symmetry analysis to the time fractional generalized fifth-order KdV equation
Author(s): Wang, Gang-wei; Liu, Xi-qiang; Zhang, Ying-yuan
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18 Issue: 9 Pages: 2321-2326 DOI: 10.1016/j.cnsns.2012.11.032 Published: SEP 2013

Title: A note on fractional electrodynamics
Author(s): Nasrolahpour, Hosein
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18 Issue: 9 Pages: 2589-2593 DOI: 10.1016/j.cnsns.2013.01.005 Published: SEP 2013

Title: Global solutions for nonlinear fuzzy fractional integral and integrodifferential equations
Author(s): Alikhani, Robab; Bahrami, Fariba
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18 Issue: 8 Pages: 2007-2017 DOI: 10.1016/j.cnsns.2012.12.026 Published: AUG 2013

Title: Mixed A(1)-A(infinity) bounds for fractional integrals
Author(s): Recchi, Jorgelina
Source: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: 403 Issue: 1 Pages: 283-296 DOI: 10.1016/j.jmaa.2013.02.018 Published: JUL 1 2013

Title: Combining differential evolution and particle swarm optimization to tune and realize fractional-order controllers
Author(s): Maione, Guido; Punzi, Antonio
Source: MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL SYSTEMS Volume: 19 Issue: 3 Pages: 277-299 DOI: 10.1080/13873954.2012.745006 Published: JUN 1 2013

Title: Random variables as pathwise integrals with respect to fractional Brownian motion
Author(s): Mishura, Yuliya; Shevchenko, Georgiy; Valkeila, Esko
Source: STOCHASTIC PROCESSES AND THEIR APPLICATIONS Volume: 123 Issue: 6 Pages: 2353-2369 DOI: 10.1016/j.spa.2013.02.015 Published: JUN 2013

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Conferences

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Special session: Fractional dynamical systems and signals

associated with 2014 IFAC World Congress

http://www.ifac2014.org/
August 24-29, 2014 in Cape Town, South Africa

(Contributed by Prof. Jocelyn Sabatier)

Call for Papers

The goal of this special session is to gather colleagues that work in the field of fractional calculus in order to present the latest results in fractional dynamical system and signal domains. Papers describing original research work that reflects the recent theoretical advances and experimental results as well as open new issues for research are invited. This session will cover the following topics (but not limited to):
- Signal analysis and filtering with fractional tools (restoration, reconstruction, analysis of fractal noises,
- Fractional modeling especially of (but not limited to) thermal systems, electrical systems (motors, transformers, skin effect, …), dielectric materials, electrochemical systems (batteries, ultracapacitors, fuel cells, …), mechanical systems (vibration insulation, viscoelastic materials, …), Biological systems (muscles, lungs, …)
- System identification (linear, non linear, MIMO methods, …)
- System implementation (fractional controllers and filters implementation, …)
- System analysis (Stability, observability, controllability, …)
- Observers
- Control (Fractional PID, CRONE, H∞, …)
- Diagnosis of fractional systems

Submission Deadline: Contributed Papers and special issues must be submitted before October 30, 2013.

Submission Guidelines
Prepare our papers according to recommendations available at
http://www.ifac2014.org/call-for-abstracts.php
Contact if you intend to participate

Jocelyn Sabatier and Stéphane Victor
IMS Laboratory
Université Bordeaux1 - IPB -UMR 5218 CNRS
351, Cours de la Libération
33405 Talence Cedex, France
Email: jocelyn.sabatier@u-bordeaux1.fr, stephane.victor@ims-bordeaux.fr

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Call for paper

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Functional Differential and Difference Equations with Applications 2013

Call for papers

The aim of this special issue is to report on the latest achievements in the qualitative and quantitative analysis of functional differential and difference equations. It will reflect both the state-of-the-art theoretical research and important recent advances in applications.

Differential and difference equations are a backbone for many applied problems encountered in mathematical biology, physics, medicine, social sciences, engineering, economy, and many other disciplines. It is important to develop new theories and methods, as well as to modify and refine the well-known techniques for the analysis of new classes of problems.
Submissions for this special issue should be of high quality and focus on the analysis of qualitative and quantitative properties of functional differential and difference equations as specified by the following list of topics currently attracting most attention. It may, however, be still extended to include some other topics related to differential and difference equations that fall within the scope of Abstract and Applied Analysis:
• Asymptotic behavior of solutions
• Periodic and almost periodic solutions
• Nonoscillation and oscillation properties
• Representation of solutions
• Boundary-value problems
• Stability theory
• Numerical algorithms and computational aspects
• Applications to real world phenomena

Before submission authors should carefully read over the journal's Author Guidelines, which are located at http://www.hindawi.com/journals/aaa/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/aaa/fddea13/ according to the following timetable:
Manuscript Due Friday, 26 July 2013
First Round of Reviews Friday, 18 October 2013
Publication Date Friday, 13 December 2013

Lead Guest Editor
• Josef Diblík, Brno University of Technology, Brno, Czech Republic
Guest Editors
• Elena Braverman, University of Calgary, Calgary, Canada
• István Györi, University of Pannonia, Veszprém, Hungary
• Yuriy Rogovchenko, University of Agder, Kristiansand, Norway
• Miroslava Růžičková, Žilina University, Žilina, Slovakia
• Ağacik Zafer, Middle East Technical University, Ankara, Turkey

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Books

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Fractional Fields and Applications (Mathématiques et Applications)

Serge Cohen, Jacques Istas

Book Description
This book focuses mainly on fractional Brownian fields and their extensions. It has been used to teach graduate students at Grenoble and Toulouse's Universities. It is as self-contained as possible and contains numerous exercises, with solutions in an appendix. After a foreword by Stéphane Jaffard, a long first chapter is devoted to classical results from stochastic fields and fractal analysis. A central notion throughout this book is self-similarity, which is dealt with in a second chapter with a particular emphasis on the celebrated Gaussian self-similar fields, called fractional Brownian fields after Mandelbrot and Van Ness's seminal paper. Fundamental properties of fractional Brownian fields are then stated and proved. The second central notion of this book is the so-called local asymptotic self-similarity (in short lass), which is a local version of self-similarity, defined in the third chapter. A lengthy study is devoted to lass fields with finite variance. Among these lass fields, we find both Gaussian fields and non-Gaussian fields, called Lévy fields. The Lévy fields can be viewed as bridges between fractional Brownian fields and stable self-similar fields. A further key issue concerns the identification of fractional parameters. This is the raison d'être of the statistics chapter, where generalized quadratic variations methods are mainly used for estimating fractional parameters. Last but not least, the simulation is addressed in the last chapter. Unlike the previous issues, the simulation of fractional fields is still an area of ongoing research. The algorithms presented in this chapter are efficient but do not claim to close the debate.

Contents
1 Introduction
2 Preliminaries
3 Self-Similarity
4 Asymptotic Self-Similarity
5 Statistics
6 Simulations

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The Weather and Climate: Emergent Laws and Multifractal Cascades

Shaun Lovejoy, Daniel Schertzer

Book Description
Advances in nonlinear dynamics, especially modern multifractal cascade models, allow us to investigate the weather and climate at unprecedented levels of accuracy. Using new stochastic modelling and data analysis techniques, this book provides an overview of the nonclassical, multifractal statistics. By generalizing the classical turbulence laws, emergent higher-level laws of atmospheric dynamics are obtained and are empirically validated over time-scales of seconds to decades and length-scales of millimetres to the size of the planet. In generalizing the notion of scale, atmospheric complexity is reduced to a manageable scale-invariant hierarchy of processes, thus providing a new perspective for modelling and understanding the atmosphere. This new synthesis of state-of-the-art data and nonlinear dynamics is systematically compared with other analyses and global circulation model outputs. This is an important resource for atmospheric science researchers new to multifractal theory and is also valuable for graduate students in atmospheric dynamics and physics, meteorology and oceanography.

Contents
1 Introduction
2 Classical turbulence, modern evidence
3 Scale-by-scale simplicity: an introduction to multiplicative cascades
4 Empirical analysis of cascades in the horizontal
5 Cascades, dimensions and codimensions
6 Vertical stratification and anisotropic scaling
7 Generalized scale invariance and cloud morphology
8 Space-time cascades and the emergent laws of the weather
9 Causal space-time cascades: the emergent laws of waves, and predictability and forecasting
10 The emergent laws of macroweather and the transition to the climate
11 The climate

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Intelligent Fractional Order Systems and Control

Indranil Pan, Saptarshi Das

Contents
1 Motivation for Application of Computational Intelligence Techniquesto Fractional Calculus Based Control Systems
2 Applied Fractional Calculus for Computational Intelligence Researchers
3 Brief Introduction to Computational Intelligence Paradigms for Fractional Calculus Researchers
4 Fractional Order Controller Tuning Using Swarm and Evolutionary Algorithms
5 Multi-objective Fractional Order Controller Design with Evolutionary Algorithms
6 Gain and Order Scheduling for Fractional Order Controllers
7 Enhancement of Fuzzy PID Controller with Fractional Calculus
8 Model Reduction and Analytical Rule Extraction with Evolutionary Algorithms
9 Model Reduction of Higher Order Systems in Fractional Order Template
10 Global Optimization Based Frequency Domain Design of Fractional Order Controllers with Iso-damping Characteristics
11 Chaos Synchronization with a Fractional Order Controller and Swarm Intelligence
　

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Journals

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Communications in Nonlinear Science and Numerical Simulation

Volume 18, Issue 11

Short Communication

No violation of the Leibniz rule. No fractional derivative
Vasily E. Tarasov

Regular Articles

Mathematical Methods

Generalized double Casoratian solutions to the four-potential isospectral Ablowitz–Ladik equation
Shouting Chen, Jianbing Zhang, Dengyuan Chen

Exact solutions of the simplified Keller–Segel model
Roman Cherniha, Maksym Didovych

Complete group classification of systems of two linear second-order ordinary differential equations
S. Moyo, S.V. Meleshko, G.F. Oguis

New maximal dimension of invariant subspaces to coupled systems with two-component equations
Junquan Song, Shoufeng Shen, Yongyang Jin, Jun Zhang

Initial value problems for arbitrary order fractional differential equations with delay
Zhihui Yang, Jinde Cao

Nonlinear Waves and Solitons

Existence and asymptotics of traveling wave fronts for a delayed nonlocal diffusion model with a quiescent stage
Kai Zhou, Yuan Lin, Qi-Ru Wang

Electrostatic wave solutions for a nonlinear coupled system in an inhomogeneous collisional dusty magnetoplasma
Zu-feng Liang, Xiao-yan Tang

Nonlinear Fluids

Fourier–Bessel theory on flow acoustics in inviscid shear pipeline fluid flow
Yong Chen, Yiyong Huang, Xiaoqian Chen

Chaos and Complexity

Spectral coarse graining of complex clustered networks
Juan Chen, Jun-an Lu, Xiaofei Lu, Xiaoqun Wu, Guanrong Chen

A novel chaos danger model immune algorithm
Qingyang Xu, Song Wang, Li Zhang, Ying Liang

Positive solutions to singular fractional differential system with coupled boundary conditions
Jiqiang Jiang, Lishan Liu, Yonghong Wu

A novel image encryption algorithm using chaos and reversible cellular automata
Xingyuan Wang, Dapeng Luan

The development and interaction of terrorist and fanatic groups
Erika T. Camacho

Transient chaos in two coupled, dissipatively perturbed Hamiltonian Duffing oscillators
S. Sabarathinam, K. Thamilmaran, L. Borkowski, P. Perlikowski, P. Brzeski, A. Stefanski, T. Kapitaniak

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Paper Highlight
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Foundation of the fractional calculus in generalized function algebras

Mirjana Stojanovic

Publication information: Mirjana Stojanovic, Foundation of the fractional calculus in generalized function algebras, Analysis and Applications, Vol. 10, No. 4 (2012) 439-467.
http://dx.doi.org/10.1142/S0219530512500212

Abstract
We introduce an approach to fractional derivatives involving singularities based on the theory of algebras of generalized functions in the sense of Colombeau. We are interested in solving fractional nonlinear ODEs and PDEs with singularities with a lack of solutions in the space of classical functions or distributions. For these purposes, we embed different forms of fractional derivatives into space of Colombeau special algebra of generalized functions using appropriate techniques such as the regularization with delta sequences and multiplication with different cut-off functions. Finally, we present an example for application of the ideas presented in paper to confirm the reason of introducing fractional derivatives into Colombeau algebra of generalized functions.

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A brief history and exposition of the fundamental theory of fractional calculus

Bertram Ross

Publication information: Bertram Ross. A brief history and exposition of the fundamental theory of fractional calculus. Fractional calculus and its applications, Lecture Notes in Mathematics, 1975, 457:1-36.
http://link.springer.com/chapter/10.1007/BFb0067096

Abstract. This opening lecture is intended to serve as a propaedeutic for the papers to be presented at this conference whose nonhomogeneous audience includes scientists, mathematicians, engineers and educators. This expository and developmental lecture, a case study of mathematical growth, surveys the origin and development of a mathematical idea from its birth in intellectual curiosity to applications. The fundamental structure of fractional calculus is outlined. The possibilities for the use of fractional calculus in applicable mathematics is indicated. The lecture closes with a statement of the purpose of the conference.

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The End of This Issue

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