FDA Express

Guest Editors
Prof. Clara Ionescu, Department of Electrical engineering, Systems and Automation, Faculty of Applied Sciences, Ghent University, Belgium
Prof. Yong Zhou, Faculty of Mathematics and Computational Science, Xiangtan University, China
Prof. J. A. Tenreiro Machado, Department of Electrical Engineering, ISEP-Institute of Engineering Polytechnic of Porto, Portugal

Subject Coverage
Optimal control and synchronization of factional order systems
Iterative learning control of fractional order systems
Dynamics and control of fractional differential equations
Modelling and simulation of fractional dynamical systems
Applications in engineering sciences

Deadline
April. 30, 2014

Submission of Manuscripts
Please kindly note that all manuscripts should be submitted electronically by using online manuscript submission at http://mc.manuscriptcentral.com/jvc. The authors should select “Special Issue: Fractional Dynamics and Control” when you reach “Manuscript Type” step in the submission process.

This specisl issue will include 10 papers. Be advised that each author will only be allowed to have one manuscripts in the special issue either as a corresponding author or contributing author.

There are no page charges.
　

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Books

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Basic Theory of Fractional Differential Equations

Yong Zhou

Book Description

This invaluable book is devoted to a rapidly developing area on the research of the qualitative theory of fractional differential equations. It is self-contained and unified in presentation, and provides readers the necessary background material required to go further into the subject and explore the rich research literature.

The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, the Picard operators technique, critical point theory and semigroups theory. Based on research work carried out by the author and other experts during the past four years, the contents are very new and comprehensive. It is useful to researchers and graduate students for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and related disciplines.

More information on this book can be found by the following link:

http://www.worldscientific.com/worldscibooks/10.1142/9069

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Fractional Calculus and Waves in Linear Vescoelasticity: An Introduction to Mathematical Models (Second Revised Edition)

Francesco Mainardi

Book Description

Fractional Calculus and Waves in Linear Viscoelasticity (Second Revised Edition) is a self-contained treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation and waves) with particular regard to models based on fractional calculus. It serves as a general introduction to the above-mentioned areas of mathematical modelling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature. In particular the relevant role played by some special functions is pointed out along with their visualization through plots. Graphics are extensively used in the book and a large general bibliography is included at the end.

This new edition has been entirely revised and updated to reflect recent developments in the field. This Second Revised Edition keeps the structure of the First Edition but all chapters and appendices have been revised and expanded.

More information on this book can be found by the following link:

http://www.allbookstores.com/Fractional-Calculus-Waves-Linear-Vescoelasticity/9781783263981

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Journals

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Fractional Calculus and Applied Analysis

Volume 17, Issue 2

Editorial

Virginia Kiryakova

On fractional lyapunov exponent for solutions of linear fractional differential equations

Nguyen Dinh Cong, Doan Thai Son, Hoang The Tuan

Numerical solution of fractional Sturm-Liouville equation in integral form

Tomasz Blaszczyk, Mariusz Ciesielski

Optimal random search, fractional dynamics and fractional calculus

Caibin Zeng, YangQuan Chen

Nonlinear multi-order fractional differential equations with periodic/anti-periodic boundary conditions

Sangita Choudhary, Varsha Daftardar-Gejji

A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations

Bashir Ahmad, Sotiris K. Ntouyas

Towards a geometric interpretation of generalized fractional integrals — Erdélyi-Kober type integrals on R N , as an example

Richard Herrmann

A new equivalence of Stefan’s problems for the time fractional diffusion equation

Sabrina Roscani, Eduardo Santillan Marcus

Numerical solutions of the initial value problem for fractional differential equations by modification of the Adomian decomposition method

Neda Khodabakhshi, S. Mansour Vaezpour

Fractional Sobolev type spaces associated with a singular differential operator and applications

Mourad Jelassi, Hatem Mejjaoli

Fractional relaxation with time-varying coefficient

Roberto Garra, Andrea Giusti

Time response analysis of fractional-order control systems: A survey on recent results

Mohammad Saleh Tavazoei

Adaptive gain-order fractional control for network-based applications

Inés Tejado, S. Hassan HosseinNia

Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications

Mohammed Al-Refai, Yuri Luchko

Existence and uniqueness of solutions for a fractional boundary value problem on a graph

John R. Graef, Lingju Kong, Min Wang

Stabilizability of fractional dynamical systems

Krishnan Balachandran, Venkatesan Govindaraj

Fractional Skellam processes with applications to finance

Alexander Kerss, Nikolai N. Leonenko

Some pioneers of the applications of fractional calculus

Duarte Valério, José Tenreiro Machado

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Communications in Nonlinear Science and Numerical Simulation

Volume 19, Issue 9 (selected)

Chaos in a new fractional-order system without equilibrium points

Donato Cafagna, Giuseppe Grassi

Numerical analysis of the initial conditions in fractional systems

J. Tenreiro Machado

Lyapunov functions for fractional order systems

Norelys Aguila-Camacho, Manuel A. Duarte-Mermoud, Javier A. Gallegos

A class of nonlinear differential equations with fractional integrable impulses

JinRong Wang, Yuruo Zhang

Nonlinear self-adjointness, conservation laws, exact solutions of a system of dispersive evolution equations

R. Tracinà, M.S. Bruzón, M.L. Gandarias, M. Torrisi

Solitons in coupled nonlinear Schrödinger equations with variable coefficients

Lijia Han, Yehui Huang, Hui Liu

Effective particle methods for Fisher–Kolmogorov equations: Theory and applications to brain tumor dynamics

Juan Belmonte-Beitia, Gabriel F. Calvo, Víctor M. Pérez-García

Computing topological entropy for periodic sequences of unimodal maps

Jose S. Cánovas, María Muñoz Guillermo

Global resonance optimization analysis of nonlinear mechanical systems: Application to the uncertainty quantification problems in rotor dynamics

Haitao Liao

Coupled Van der Pol oscillator with non-integer order connection

L. Cveticanin

High-order solutions around triangular libration points in the elliptic restricted three-body problem and applications to low energy transfers

Hanlun Lei, Bo Xu

Transient times, resonances and drifts of attractors in dissipative rotational dynamics

Alessandra Celletti, Christoph Lhotka

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Entropy

Volume 16 Issue 4

An Entropy-Based Contagion Index and Its Sampling Properties for Landscape Analysis

by Bernard R. Parresol and Lloyd A. Edwards

A Study of Fractality and Long-Range Order in the Distribution of Transposable Elements in Eukaryotic Genomes Using the Scaling Properties of Block Entropy and Box-Counting

Labrini Athanasopoulou, Diamantis Sellis and Yannis Almirantis

District Heating Mode Analysis Based on an Air-cooled Combined Heat and Power Station

Pei Feng Li, Zhihua Ge, Zhiping Yang, Yuyong Chen and Yongping Yang

A Dynamic Dark Information Energy Consistent with Planck Data

Michael Paul Gough

The Entropy Production Distribution in Non-Markovian Thermal Baths

José Inés Jiménez-Aquino and Rosa María Velasco

Information in Biological Systems and the Fluctuation Theorem

Yaşar Demirel

Topological Classification of Limit Cycles of Piecewise Smooth Dynamical Systems and Its Associated Non-Standard Bifurcations

John Alexander Taborda and Ivan Arango

Stochastic Dynamics of Proteins and the Action of Biological Molecular Machines

Michal Kurzynski and Przemyslaw Chelminiak

Retraction: Zheng, T. et al. Effect of Heat Leak and Finite Thermal Capacity on the Optimal Configuration of a Two-Heat-Reservoir Heat Engine for Another Linear Heat Transfer Law. Entropy 2003, 5, 519–530

Kevin H. Knuth

Intersection Information Based on Common Randomness

Virgil Griffith, Edwin K. P. Chong, Ryan G. James, Christopher J. Ellison and James P. Crutchfield

A Fuzzy Parallel Processing Scheme for Enhancing the Effectiveness of a Dynamic Just-in-time Location-aware Service System

Toly Chen

Matrix Algebraic Properties of the Fisher Information Matrix of Stationary Processes

André Klein

Entropy and Exergy Analysis of a Heat Recovery Vapor Generator for Ammonia-Water Mixtures

Kyoung Hoon Kim, Kyoungjin Kim and Hyung Jong Ko

The Entropic Potential Concept: a New Way to Look at Energy Transfer Operations

Tammo Wenterodt and Heinz Herwig

Cross Layer Interference Management in Wireless Biomedical Networks

Emmanouil G. Spanakis, Vangelis Sakkalis, Kostas Marias and Apostolos Traganitis

Wiretap Channel with Information Embedding on Actions

Xinxing Yin and Zhi Xue

Information Geometry of Positive Measures and Positive-Definite Matrices: Decomposable Dually Flat Structure

Shun-ichi Amari

Possible Further Evidence for the Thixotropic Phenomenon of Water

Nada Verdel and Peter Bukovec

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Paper Highlight
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Fractional advection-dispersion equations for modeling transport at the Earth surface

R. Schumer, M. M. Meerschaert, and B. Baeumer

Publication information: R. Schumer, M. M. Meerschaert, and B. Baeumer (2009), Fractional advection-dispersion equations for modeling transport at the Earth surface, J. Geophys. Res., 114, F00A07, doi:10.1029/2008JF001246. http://www.agu.org/pubs/crossref/2009/2008JF001246.shtml

Abstract

Characterizing the collective behavior of particle transport on the Earth surface is a key ingredient in describing landscape evolution. We seek equations that capture essential features of transport of an ensemble of particles on hillslopes, valleys, river channels, or river networks, such as mass conservation, superdiffusive spreading in flow fields with large velocity variation, or retardation due to particle trapping. Development of stochastic partial differential equations such as the advection-dispersion equation (ADE) begins with assumptions about the random behavior of a single particle: possible velocities it may experience in a flow field and the length of time it may be immobilized. When assumptions underlying the ADE are relaxed, a fractional ADE (fADE) can arise, with a non-integer-order derivative on time or space terms. Fractional ADEs are nonlocal; they describe transport affected by hydraulic conditions at a distance. Space fractional ADEs arise when velocity variations are heavy tailed and describe particle motion that accounts for variation in the flow field over the entire system. Time fractional ADEs arise as a result of power law particle residence time distributions and describe particle motion with memory in time. Here we present a phenomenological discussion of how particle transport behavior may be parsimoniously described by a fADE, consistent with evidence of superdiffusive and subdiffusive behavior in natural and experimental systems.

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Fractional calculus in hydrologic modeling: A numerical perspective

David A. Benson, Mark M. Meerschaert, Jordan Revielle

Publication information: David A. Benson, Mark M. Meerschaert, Jordan Revielle, Fractional calculus in hydrologic modeling: A numerical perspective, Advances in Water Resources, 2013, 51, 479-497. http://www.sciencedirect.com/science/article/pii/S0309170812000899

Abstract

Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus.

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The End of This Issue

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