FDA Express (Vol.8, No.1, Jul.15, 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: Pricing currency options in the mixed fractional Brownian motion
Author(s): Sun, Lin
Source: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS Volume: 392 Issue: 16 Pages: 3441-3458 DOI: 10.1016/j.physa.2013.03.055 Published: AUG 15 2013

Title: Superlinearly convergent algorithms for the two-dimensional space-time Caputo-Riesz fractional diffusion equation
Author(s): Chen, Minghua; Deng, Weihua; Wu, Yujiang
Source: APPLIED NUMERICAL MATHEMATICS Volume: 70 Pages: 22-41 DOI: 10.1016/j.apnum.2013.03.006 Published: AUG 2013

Title: Improved approximate methods for calculating frequency response function matrix and response of MDOF systems with viscoelastic hereditary terms
Author(s): Li, Li; Hu, Yujin; Wang, Xuelin
Source: JOURNAL OF SOUND AND VIBRATION Volume: 332 Issue: 15 Pages: 3945-3956 DOI: 10.1016/j.jsv.2013.01.043 Published: JUL 22 2013

Title: Dynamic analysis of a class of fractional-order neural networks with delay
Author(s): Chen, Liping; Chai, Yi; Wu, Ranchao; et al.
Source: NEUROCOMPUTING Volume: 111 Pages: 190-194 DOI: 10.1016/j.neucom.2012.11.034 Published: JUL 2 2013

Title: Robust synchronization for a class of fractional-order dynamical system via linear state variable
Author(s): Li, C.; Xiong, J.; Li, W.; et al.
Source: INDIAN JOURNAL OF PHYSICS Volume: 87 Issue: 7 Pages: 673-678 DOI: 10.1007/s12648-013-0267-7 Published: JUL 2013

Title: Gradient Estimates of q-Harmonic Functions of Fractional Schrodinger Operator
Author(s): Kulczycki, Tadeusz
Source: POTENTIAL ANALYSIS Volume: 39 Issue: 1 Pages: 69-98 DOI: 10.1007/s11118-012-9322-9 Published: JUL 2013

Title: Quasi-Compact Finite Difference Schemes for Space Fractional Diffusion Equations
Author(s): Zhou, Han; Tian, WenyYi; Deng, Weihua
Source: JOURNAL OF SCIENTIFIC COMPUTING Volume: 56 Issue: 1 Pages: 45-66 DOI: 10.1007/s10915-012-9661-0 Published: JUL 2013

Title: Profile decompositions and blowup phenomena of mass critical fractional Schrodinger equations
Author(s): Cho, Yonggeun; Hwang, Gyeongha; Kwon, Soonsik; et al.
Source: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS Volume: 86 Pages: 12-29 DOI: 10.1016/j.na.2013.03.002 Published: JUL 2013

Title: IIR approximations to the fractional differentiator/integrator using Chebyshev polynomials theory.
Author(s): Romero, M; de Madrid, A P; Manoso, C; et al.
Source: ISA transactions Volume: 52 Issue: 4 Pages: 461-8 DOI: 10.1016/j.isatra.2013.02.002 Published: 2013-Jul (Epub 2013 Mar 15)

Title: Enhanced robust fractional order proportional-plus-integral controller based on neural network for velocity control of permanent magnet synchronous motor.
Author(s): Zhang, Bitao; Pi, Youguo
Source: ISA transactions Volume: 52 Issue: 4 Pages: 510-6 DOI: 10.1016/j.isatra.2013.02.003 Published: 2013-Jul (Epub 2013 Mar 08)

Title: Performance comparison of optimal fractional order hybrid fuzzy PID controllers for handling oscillatory fractional order processes with dead time.
Author(s): Das, Saptarshi; Pan, Indranil; Das, Shantanu
Source: ISA transactions Volume: 52 Issue: 4 Pages: 550-66 DOI: 10.1016/j.isatra.2013.03.004 Published: 2013-Jul (Epub 2013 May 07)

Title: An application of fractional differintegration to heart rate variability time series.
Author(s): Garcia-Gonzalez, Miguel A; Fernandez-Chimeno, Mireya; Capdevila, Lluis; et al.
Source: Computer methods and programs in biomedicine Volume: 111 Issue: 1 Pages: 33-40 DOI: 10.1016/j.cmpb.2013.02.009 Published: 2013-Jul

Title: Finite element method for two-dimensional time-fractional tricomi-type equations
Author(s): Zhang, Xindong; Huang, Pengzhan; Feng, Xinlong; et al.
Source: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS Volume: 29 Issue: 4 Pages: 1081-1096 DOI: 10.1002/num.21745 Published: JUL 2013

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Conferences

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International Conference on Fractional Differentiation and Its Applications (ICFDA’14)

June 23-25, 2014, University of Catania, Catania, Italy

The organizing committee of ICFDA’14 extends a cordial invitation to you to come to Catania to meet renowned scholars and practitioners from all over the world.

Scope
The scope of the conference is to present the state of the art on fractional systems, both on theoretical and application aspects. The growing research and development on fractional calculus in the areas of mathematics, physics and engineering, both from university and industry, motivates this international event gathering and unifying the whole community.

Topics
Major topics include but are not limited on fractional differentiation in: Acoustic Dissipation, Anomalous diffusion, Applications of fractional systems, Biomedical Engineering, Computational Fractional Derivative Equations, Continuous Time Random Walk, Control, Creep, Filters, Fractal Derivative and Fractals, Fractional Brownian Motion, Geophysics, History dependent Process, History of Fractional Calculus, Levy Statistics, Modeling and identification, Non-Fourier Heat Conduction, Nonlocal Phenomena, Phase-Locked Loops, Porous Media, Power Law, Relaxation, Rheology, Riesz Potential, Signal and Imaging Processing, Singularities Analysis and Integral Representations for Fractional Differential Systems, Soft Matter Mechanics, Special Functions and Integral Transforms Related to Fractional Calculus, Stretched Gaussian, Variational Principles, Vibration, Viscoelasticity.

Timetable
Invited session submission November 1th, 2013
Regular and invited paper submission November 10th, 2013
Notification of acceptance February 15th, 2014
Final submission March 31th, 2014
Conference June 23th - 25th, 2014
Early registration April 10th, 2014

For more details please refer to:
http://www.icfda14.dieei.unict.it/timetable.html

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MESA Lab Presents Fractional Calculus Day @ UCMerced

Contributed by Prof. YangQuan Chen

http://mechatronics.ucmerced.edu/news/2013/fractional-calculus-day-ucmerced

Fractional calculus (FC) is about differentiation or integration of non-integer orders. The concept of fractional calculus has tremendous potential to change the way we see, model, and control the nature around us. Using integer order calculus, behaviors of many complex systems are being said to be "anomalous" such as "anomalous relaxation", "anomalous diffusion" etc. It has already been known that "anomalous is normal" from observation and modeling point of view if fractional calculus is used. Meanwhile, beneficial uses of the mathematical tool of fractional calculus from engineering point of view are being shown and (hopefully) fractional calculus will become an enabler for new science discoveries.

See the Fractional Calculus Day website for more details.

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Books

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Advances in the Theory and Applications of Non-integer Order Systems: 5th Conference on Non-integer Order Calculus and Its Applications, Cracow, Poland
(Lecture Notes in Electrical Engineering)

Editor: Wojciech Mitkowski , Janusz Kacprzyk ,Jerzy Baranowski

Book Description
This volume presents various aspects of non-integer order systems, also known as fractional systems, which have recently attracted an increasing attention in the scientific community of systems science, applied mathematics, control theory. Non-integer systems have become relevant for many fields of science and technology exemplified by the modeling of signal transmission, electric noise, dielectric polarization, heat transfer, electrochemical reactions, thermal processes, acoustics, etc. The content is divided into six parts, every of which considers one of the currently relevant problems. In the first part the Realization problem is discussed, with a special focus on positive systems. The second part considers stability of certain classes of non-integer order systems with and without delays. The third part is focused on such important aspects as controllability, observability and optimization especially in discrete time. The fourth part is focused on distributed systems where non-integer calculus leads to new and interesting results. The next part considers problems of solutions and approximations of non-integer order equations and systems. The final and most extensive part is devoted to applications. Problems from mechatronics, biomedical engineering, robotics and others are all analyzed and solved with tools from fractional systems. This volume came to fruition thanks to high level of talks and interesting discussions at RRNR 2013 - 5th Conference on Non-integer Order Calculus and its Applications that took place at AGH University of Science and Technology in Kraków, Poland, which was organized by the Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering.

Contents
Preface
Part I Realization Problem
Part II Stability
Part III Controllability, Observability and Optimal Control
Part IV Distributed Parameter Systems
Part V Solutions and Approximations
Part VI Applications

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Control and Optimization with PDE Constraints (International Series of Numerical Mathematics)

Editor: Kristian Bredies , Christian Clason , Karl Kunisch , Gregory Winckel

Book Description
Many mathematical models of physical, biological and social systems involve partial differential equations (PDEs). The desire to understand and influence these systems naturally leads to considering problems of control and optimization. This book presents important topics in the areas of control of PDEs and of PDE-constrained optimization, covering the full spectrum from analysis to numerical realization and applications. Leading scientists address current topics such as non-smooth optimization, Hamilton–Jacobi–Bellmann equations, issues in optimization and control of stochastic partial differential equations, reduced-order models and domain decomposition, discretization error estimates for optimal control problems, and control of quantum-dynamical systems. These contributions originate from the “International Workshop on Control and Optimization of PDEs” in Mariatrost in October 2011. This book is an excellent resource for students and researchers in control or optimization of differential equations. Readers interested in theory or in numerical algorithms will find this book equally useful.

Contents
An adaptive POD Approximation Method for the Control of Advection-Diffusion Equations
Generalized Sensitivity Analysis for Delay Differential Equations
Regularity and Unique Existence of Solution to Linear Diffusion Equation with Multiple Time-fractional Derivative
Nonsmooth Optimization Method and Sparsity
Parareal in Time Intermediate Targets Methods for Optimal Control Problems
Hamilton-Jacobi-Bellman Equations on Multi-domains
Gradient Computation for Model Calibration with Pointwise Observations
Numerical Analysis of POD A-posterior Error Estimation for Optimal Control
Cubature on C1 Spcae
A Globalized Newton Method for the Optimal Control of Fermionic Systems
A Prior Error Estimates for Optimal Control Problems with Constraints on the Gradient of the State on Nonsmooth Polygonal Domains

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Journals

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Communications in Nonlinear Science and Numerical Simulation

Volume 18, Issue 12

Regular Articles

A new linearized compact multisplitting scheme for the nonlinear convection–reaction–diffusion equations with delay
Qifeng Zhang, Chengjian Zhang

Existence result of solutions to differential equations of variable-order with nonlinear boundary value conditions
Shuqin Zhang

Group invariant solution for a pre-existing fracture driven by a power-law fluid in impermeable rock
A.G. Fareo, D.P. Mason

Computation of partially invariant solutions for the Einstein Walker manifolds’ identifying equations
Mehdi Nadjafikhah, Mehdi Jafari

Novel rogue waves in an inhomogenous nonlinear medium with external potentials
Xiao-Fei Wu, Guo-Sheng Hua, Zheng-Yi Ma

On rogue wave in the Kundu-DNLS equation
Shibao Shan, Chuanzhong Li, Jingsong He

Backbone fractal dimension and fractal hybrid orbital of protein structure
Xin Peng, Wei Qi, Mengfan Wang, Rongxin Su, Zhimin He

Environmental dispersion in a three-layer wetland flow with free-surface
P. Wang, Zi Wu, G.Q. Chen, B.S. Cui

Magnetohydrodynamic free convection flow above an isothermal horizontal plate
Subho Samanta, Abhijit Guha

Statistics of Poincaré recurrences in local and global approaches
Vadim S. Anishchenko, Sergey V. Astakhov, Yaroslav I. Boev, Nadezhda I. Biryukova, Galina I. Strelkova

Controlling unpredictability in the randomly driven Hénon–Heiles system
Mattia Coccolo, Jesús M. Seoane, Miguel A.F. Sanjuán

Approximate controllability of nonlinear fractional dynamical systems
R. Sakthivel, R. Ganesh, Yong Ren, S.M. Anthoni

Models and numerical schemes for generalized van der Pol equations
Yufeng Xu, Om P. Agrawal

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Journal of Applied Nonlinear Dynamics

Volume 2, Issue 2

Stability Boundaries of Period-1 Rotation for a Pendulum Under Combined Vertical and Horizontal Excitation
B. Horton, S. Lenci, E. Pavlovskaia, F. Romeo, G. Rega, and M. Wiercigroch

Simple Geometric Techniques to Delineate the Location, Extent, and Approximate Shapes of Attractors in Chaotic Systems
S. Roy Choudhury

Self-Similar Property of Random Signals: Solution of Inverse Problem
Raoul R. Nigmatullin and J.A. Tenreiro Machado

Some Remarks on a Multi Point Boundary Value Problem for a Fractional Order Differential Inclusion
Aurelian Cernea

Rolling of a Rigid Body Without Slipping and Spinning: Kinematics and Dynamics
A.V. Borisov, I.S. Mamaev, and D.V. Treschev

Influence of Embedded Material on Natural Frequencies of Double Segment Rotating Disk
Ehsan Sarfaraz and Hamid R. Hamidzadeh

Alternate Models of Replicator Dynamics
Elizabeth N. Wesson and Richard H. Rand

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Paper Highlight
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Pitfalls in single particle tracking in living cells

Ralf Metzler, Yong He, Stas Burov, Eli Barkai

Publication information:
Ralf Metzler, Yong He, Stas Burov, Eli Barkai, Pitfalls in single particle tracking in living cells, Biophysical Journal, 96(3), 2009, 385a.
http://www.sciencedirect.com/science/article/pii/S0006349508031081

Abstract
An increasing body of evidence for subdiffusion of biopolymers under typical in vivo conditions has been reported recently. The physical foundation of this subdiffusion remains unidentified although it is commonly ascribed to molecular crowding. Single particle tracking provides crucial information on the mechanisms behind the subdiffusion. In several such experiments the measured mean squared displacement shows a characteristic scatter (e.g., [1,2]).

Using the widely accepted continuous time random walk framework we demonstrate that pronounced scatter in time averaged quantities such as the mean squared displacement is no artefact but arises naturally from the nonexistence of a characteristic time scale separating microscopic and macroscopic events [3,4]. An expression for the broad distribution of diffusion coefficients in such measurements is derived and confirmed by simulations. The most crucial finding from our theory is that the subdiffusive nature of the particles will be masked in the time averages: What looks like normal diffusion in an experiment may in reality be subdiffusion in an ageing system. Interpretations of the reported data in [1,2] will be discussed. We provide general guidelines to properly intepret single molecule tracking data.

We also argue that ageing properties in biopolymer diffusion in living cells may be advantageous for the accuracy of genetic regulation at minimal concentrations of transcription factors. The physical picture emerging from our theory provides additional support for a more local picture of gene regulation and confirms the importance of colocalisation in the genome.

[1] I. Golding and E.C. Cox, Phys. Rev. Lett. 96, 098102 (2006).
[2] I.M. Tolic-Noerrelykke et al, Phys. Rev. Lett. 93, 078102 (2004).
[3] Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. 101, 058101 (2008).
[4] M.A. Lomholt, I.M. Zaid, and R. Metzler, Phys. Rev. Lett. 98, 200603 (2007).

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Quantitative analysis of single particle trajectories: mean maximal excursion method

Vincent Tejedor. Olivier Bénichou, Raphael Voituriez, Ralf Jungmann, Friedrich Simmel, Christine Selhuber-Unkel, Lene B. Oddershede, Ralf Metzler

Publication information:
Vincent Tejedor. Olivier Bénichou, Raphael Voituriez, Ralf Jungmann, Friedrich Simmel, Christine Selhuber-Unkel, Lene B. Oddershede, Ralf Metzler. Quantitative Analysis of Single Particle Trajectories: Mean Maximal Excursion Method. Biophysical Journal, 98(7), 2010, 1364-1372.
http://www.sciencedirect.com/science/article/pii/S0006349509060974

Abstract.
An increasing number of experimental studies employ single particle tracking to probe the physical environment in complex systems. We here propose and discuss what we believe are new methods to analyze the time series of the particle traces, in particular, for subdiffusion phenomena. We discuss the statistical properties of mean maximal excursions (MMEs), i.e., the maximal distance covered by a test particle up to time t. Compared to traditional methods focusing on the mean-squared displacement we show that the MME analysis performs better in the determination of the anomalous diffusion exponent. We also demonstrate that combination of regular moments with moments of the MME method provides additional criteria to determine the exact physical nature of the underlying stochastic subdiffusion processes. We put the methods to test using experimental data as well as simulated time series from different models for normal and anomalous dynamics such as diffusion on fractals, continuous time random walks, and fractional Brownian motion.

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The End of This Issue

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