FDA Express Vol. 3, No. 6, Jun. 30, 2012
Editors:
W. Chen H.G. Sun
X.D. Zhang
S. Hu
Institute of Soft Matter Mechanics, Hohai University
For contribution: fdaexpress@163.com,
fdaexpress@hhu.edu.cn
For subscription:
http://em.hhu.edu.cn/fda/subscription.htm
◆ Updated Information
Researchers & Groups: Prof. Virginia Kiryakova
◆ Conferences
1st International Conference on Frontiers in Computational Physics: Modeling the Earth System
◆ Books
Fractional Order Motion Controls
Introduction to the Fractional Calculus of Variations
◆ Journals
Communications in Nonlinear Science and Numerical Simulation
Fractional Calculus and
Applied Analysis
◆ Classical Papers
Basic theory of
fractional differential equations
Fractional Cauchy problems on bounded domains
◆ Researchers & Groups
========================================================================
Updated
Information
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Researchers &
Groups: Prof. Virginia Kiryakova
Below is the updated list of "selected papers" by Prof. Virginia Kiryakova:
Criteria for
univalence of the Dziok-Srivastava and the Srivastava-Wright operators in the
class A
Kiryakova Virginia
APPLIED MATHEMATICS AND COMPUTATION Volume: 218 Issue: 3 Special Issue: SI
Pages: 883-892, DOI: 10.1016/j.amc.2011.01.076, Published: OCT 1 2011
Recent history of
fractional calculus
Machado J. Tenreiro; Kiryakova Virginia; Mainardi Francesco
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 16 Issue: 3
Pages: 1140-1153, DOI: 10.1016/j.cnsns.2010.05.027, 2011
The multi-index
Mittag-Leffler functions as an important class of special functions of
fractional calculus
Kiryakova Virginia
COMPUTERS & MATHEMATICS WITH APPLICATIONS Volume: 59 Issue: 5 Special Issue: SI
Pages: 1885-1895, DOI: 10.1016/j.camwa.2009.08.025, 2010
The special
functions of fractional calculus as generalized fractional calculus operators of
some basic functions
Kiryakova Virginia
COMPUTERS & MATHEMATICS WITH APPLICATIONS Volume: 59 Issue: 3 Pages: 1128-1141,
DOI: 10.1016/j.camwa.2009.05.014, 2010
A brief story about the operators of
generalized fractional calculus
Kiryakova Virginia
FRACT. CALC. APPL. ANAL. Volume: 11 Issue: 2 Pages: 203-220
http://www.math.bas.bg/~fcaa/volume11/fcaa112/Kiryakova_fcaa112.pdf, Published:
2008
Solutions of fractional
multi-order integral and differential equations using a Poisson-type transform
Ali Ismail; Kiryakova Virginia;
Kalla Shyam L
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: Issue: 1
Pages: 172-199, DOI: 10.1016/S0022-247X(02)00012-4, Published: 2002
A multi-index
Borel-Dzrbashjan transform
Al-Musallam F, Kiryakova V, Tuan VK
ROCKY MOUNTAIN JOURNAL OF
MATHEMATICS Volume: 32 Issue: 2 Pages: 409-428, DOI: 10.1216/rmjm/1030539678, Published: 2002
The Obrechkoff integral transform:
Properties and relation to a generalized fractional calculus
Dimovski I.; Kiryakova, V
NUMERICAL FUNC. ANAL. AND OPTIMIZATION Volume: 21
Issue: No 1-2 Pages 121-144, DOI: 10.1080/01630560008816944, Published: 2000
All
the special functions are fractional
differintegrals of elementary functions
Kiryakova Virginia
J. PHYSICS A: MATH. & GENERAL Volume:
30, Issue: 14
Pages: 5085-5103,
DOI:
10.1088/0305-4470/30/14/019, Published: 1997
========================================================================
Conferences
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
1st International Conference on Frontiers in Computational Physics: Modeling the Earth System
Abstract submission deadline - 13 July 2012
Boulder, CO, USA 16 - 20 December 2012
Computational science complements the classical paradigm of theory and observation, and leads where neither is available. In particular, computational models play an essential role in diagnosis and prognosis of all elements of the Earth System, from solar variablity through space weather, geomechanics, terrestrial climate and weather, down to ground water flow. This inaugural four-day Conference on Frontiers in Computational Physics will provide a forum for exchanging and sharing experiences, knowledge and on advanced computational techniques, methods, and models for simulation of the Earth System. With computational aspects in focus, the physical emphasis is on natural problems that are complex, coupled and multiscale.
-Global systems and complexity models
-Global and regional climate, uncertainty quantification
-Solar variability and space weather
-Weather, deep atmosphere, planetary boundary layer, air quality
-Ocean, anisotropy, eddy resolving computations
-Water cycle, glaciology, ground water flow
-Geology and geomechanics
-Multiscale interactions, turbulence, extreme events, subgrid-scale parameterizations
The conference will consist of several plenary invited talks, together with contributions from all fields above, organized in parallel sessions. A part of sessions will be reserved for "topical sessions" proposed by their conveners.
A call for papers related to the conference theme will be made shortly after the meeting; these papers will be considered for publication, undergoing the usual review process, in a topical issue of the Journal of Computational Physics.
==========================================================================
Books
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Ying Luo, YangQuan Chen
http://as.wiley.com/WileyCDA/WileyTitle/productCd-1119944554.html
Covering fractional order theory, simulation and experiments, this book explains how fractional order modelling and fractional order controller design compares favourably with traditional velocity and position control systems. The authors systematically compare the two approaches using applied fractional calculus. Stability theory in fractional order controllers design is also analysed.
The book also covers key topics including: fractional order disturbance cancellation and adaptive learning control studies for external disturbances; optimization approaches for nonlinear system control and design schemes with backlash and friction. Illustrations and experimental validations are included for each of the proposed control schemes to enable readers to develop a clear understanding of the approaches covered, and move on to apply them in real-world scenarios.
Table of contents
PART I FUNDAMENTALS OF FRACTIONAL CONTROLS
1 Introduction
PART II FRACTIONAL ORDER VELOCITY SERVO
2 Fractional
Order PI Controller Designs for Velocity Servo Systems
3 Tuning Fractional Order PI
Controllers for Fractional Order Velocity
Systems with Experimental Validation
4 Relay Feedback Tuning of Robust PID Controllers
5 Auto-Tuning of Fractional Order Controllers with Iso-Damping
PART III FRACTIONAL ORDER POSITION SERVO
6 Fractional Order PD Controller Tuning for Position Systems
7 Fractional Order [PD] Controller Synthesis for Position Servo Systems
8 Time-Constant Robust Analysis and Design of Fractional Order [PD] Controller
9 Experimental Study of Fractional OrderPDController Synthesis for Fractional Order Position Servo Systems
10 Fractional Order [PD] Controller Design and Comparison for Fractional Order Position Servo Systems
PART IV STABILITY AND FEASIBILITY FOR FOPID DESIGN
11 Stability and Design Feasibility of Robust PID Controllers for FOPTD Systems
12 Stability and Design Feasibility of Robust FOPI Controllers for FOPTD Systems
PART V FRACTIONAL ORDER DISTURBANCE COMPENSATORS
13 Fractional Order Disturbance Observer
14 Fractional Order Adaptive Feed-forward Cancellation
15 Fractional Order Robust Control for Cogging Effect
16 Fractional Order Periodic Adaptive Learning Compensation
PART VI EFFECTS OF FRACTIONAL ORDER CONTROLS ON NONLINEARITIES
17 Fractional Order PID Control of A DC-Motor with Elastic Shaft
18 Fractional Order Ultra Low-Speed Position Servo
19 Optimized Fractional Order Conditional Integrator
PART VII FRACTIONAL ORDER CONTROL APPLICATIONS
20 Lateral Directional Fractional Order Control of A Small Fixed-Wing UAV
21 Fractional Order PD Controller Synthesis and Implementation for HDD Servo System
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Delfim F M Torres, Agnieszka B Malinowska
http://www.worldscibooks.com/mathematics/p871.html
This invaluable book provides a broad introduction to the fascinating and beautiful subject of Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non-conservative systems in mechanics. The inclusion of non-conservatism is extremely important from the point of view of applications. Forces that do not store energy are always present in real systems. They remove energy from the systems and, as a consequence, Noether's conservation laws cease to be valid. However, it is still possible to obtain the validity of Noether's principle using FCV. The new theory provides a more realistic approach to physics, allowing us to consider non-conservative systems in a natural way. The authors prove the necessary Euler–Lagrange conditions and corresponding Noether theorems for several types of fractional variational problems, with and without constraints, using Lagrangian and Hamiltonian formalisms. Sufficient optimality conditions are also obtained under convexity, and Leitmann's direct method is discussed within the framework of FCV.
The book is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and ambitious undergraduates in mathematics and mechanics. It provides an opportunity for an introduction to FCV for experienced researchers. The explanations in the book are detailed, in order to capture the interest of the curious reader, and the book provides the necessary background material required to go further into the subject and explore the rich research literature.
Table of contents
Readership: Advanced undergraduate, graduate students and researchers in mathematics, physics, operations research and applied sciences.
==========================================================================
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Volume 45, Issue 7
Robust filtering of uncertain stochastic genetic regulatory networks with
time-varying delays
Two characteristics of planar intertwined basins of attraction
On the nesting of Painlevé hierarchies: A Hamiltonian approach
Three-dimensional modulation of electron-acoustic waves: 3 + 1 Davey–Stewartson
system
Global stability analysis of epidemiological models based on Volterra–Lyapunov
stable matrices
Multiscale recurrence analysis of long-term nonlinear and nonstationary time
series
Chaos evidence in catecholamine secretion at chromaffin cells
Periodic and chaotic synchronizations of two distinct dynamical systems under
sinusoidal constraints
Describing some characters of serine proteinase using fractal analysis
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Communications in Nonlinear Science and Numerical Simulation
Volume 17, Issue 11
Short Communications
Asymptotic bubble evolutions of the Rayleigh–Taylor instability
Stochastic control of attractor preference in a multistable system
Articles
K. Karthikeyan, J.J. Trujillo
The finite-dimensional super integrable system of a super NLS-mKdV equation
Lie symmetries and conservation laws of the Hirota–Ramani equation
Almost automorphic solutions to some damped second-order differential equations
Hyperbolic and trigonometric solutions for some nonlinear evolution equations
Solution of the Thomas–Fermi equation with a convergent approach
A KdV-like advection–dispersion equation with some remarkable properties
Unsteady flow and heat transfer in a thin film of Ostwald–de Waele liquid over a
stretching surface
On the paradoxical behavior of a cyclic device working with a non-Boltzmannian
fluid
Effects of slip on steady Bödewadt flow of a non-Newtonian fluid
Formation patterns at the air-grain interfaces in spinning granular films at
high rotation rates
Numerical solutions of transonic two-dimensional flows at a ninety-degree wedge
Information dynamics algorithm for detecting communities in networks
Algebraic approach for the exploration of the onset of chaos in discrete
nonlinear dynamical systems
Transient chaos and crisis phenomena in butterfly valves driven by solenoid
actuators
Active sliding observer scheme based fractional chaos synchronization
On the natural solution of an impulsive fractional differential equation of
order q ∈ (1, 2)
A new synchronization algorithm for delayed complex dynamical networks via
adaptive control approach
Projective lag synchronization of the general complex dynamical networks with
distinct nodes
A modified coupled map car following model and its traffic congestion analysis
Modelling and properties of a nonlinear autonomous switching system in fed-batch
culture of glycerol
Optimal sliding mode control of single degree-of-freedom hysteretic structural
system
Parametric resonance in the Rayleigh–Duffing oscillator with time-delayed
feedback
Letters to the Editors
Periodic wave solutions of coupled integrable dispersionless equations by
residue harmonic balance
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Fractional Calculus and Applied Analysis
http://www.springerlink.com/content/1311-0454
Temporary FREE Access to:
Volume 14, Issue 1, 2011 and Volume 15, Issue 2, 2012
New issue: Volume 15, Issue 3, 2012 – Contents:
FCAA related meetings, books, in memoriam (FCAA – Volume 15 – No 3)
Virginia Kiryakova (Editorial Note)
State space solution of implicit fractional continuous time systems
Djillali Bouagada, Paul Van Dooren
Fractional differential inclusions with fractional separated boundary
conditions
Bashir Ahmad, Sotiris K. Ntouyas
Spectral approximations to the fractional integral and derivative
Changpin Li, Fanhai Zeng, Fawang Liu
Towards a combined fractional mechanics and quantization
Agnieszka B. Malinowska, Delfim F. M. Torres
A fractional imbedding theorem
Dariusz Idczak, Stanislaw Walczak
Velocity and displacement correlation functions for fractional generalized
Langevin equations
Trifce Sandev, Ralf Metzler, Zivorad Tomovski
Anti-periodic fractional boundary value problems with nonlinear term
depending on lower order derivative
Bashir Ahmad, Juan J. Nieto
Product rule for vector fractional derivatives
Diogo Bolster, Mark M. Meerschaert, Alla Sikorskii
The fBm-driven Ornstein-Uhlenbeck process: Probability density function and
anomalous diffusion
Caibin Zeng, YangQuan Chen, Qigui Yang
A Fourier generalized convolution transform and applications to integral
equations
Nguyen Xuan Thao, Vu Kim Tuan, Nguyen Thanh Hong
Uniqueness of positive solutions of fractional boundary value problems with
non-homogeneous integral boundary conditions
John R. Graef, Lingju Kong, Qingkai Kong, Min Wang
========================================================================
Basic theory of fractional differential equations
V. Lakshmikanthama, A.S. Vatsala
Publication information: V. Lakshmikanthama, A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Analysis: Theory, Methods & Applications, 2008, 69(8), 2677-2682. http://www.sciencedirect.com/science/article/pii/S0362546X07005834
Abstract. In this paper, the basic theory for the initial value problem of fractional differential equations involving Riemann-Liouville differential operators is discussed employing the classical approach. The theory of inequalities, local existence, extremal solutions, comparison result and global existence of solutions are considered.
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Fractional Cauchy problems on bounded domains
Mark M. Meerschaert, Erkan Nane, and P. Vellaisamy
Publication information:
Mark M. Meerschaert, Erkan Nane,
and P. Vellaisamy: Fractional Cauchy problems on bounded domains.
Ann. Probab.,
2009, 37(3), 979-1007.
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aop/1245434026
Abstract
Fractional Cauchy problems replace the usual first-order time derivative by a fractional derivative. This paper develops classical solutions and stochastic analogues for fractional Cauchy problems in a bounded domain D⊂ℝd with Dirichlet boundary conditions. Stochastic solutions are constructed via an inverse stable subordinator whose scaling index corresponds to the order of the fractional time derivative. Dirichlet problems corresponding to iterated Brownian motion in a bounded domain are then solved by establishing a correspondence with the case of a half-derivative in time.
========================================================================
Chair for Theoretical Physics, Inst for Physics & Astronomy, University of
Potsdam, 14476 Potsdam-Golm, Germany;
Finland Distinguished Professor, Physics Dept, Tampere University of Technology,
Korkeakoulunkatu 3, FIN-33101 Tampere, Finland .
Emailbox: metz@ph.tum.de
A Short Outline of His Life
Ralf Metzler studied at the University of Ulm, Germany, where he also received his PhD under the supervision of Theo Nonnenmacher. 1998 Ralf moved to Tel Aviv University to postdoc with Joseph Klafter. In 2000 he continued as visiting scientist at the University of Illinois at Urbana-Champaign, and as postdoc at MIT in Cambridge, MA, with Mehran Kardar. In 2002 Ralf assumed an assistant professorship at the Nordic Institute for Theoretical Physics (NORDITA), then in Copenhagen, Denmark.
After a short period as associate professor and Canada Research Chair at the
University of Ottawa, ON, in 2007 Ralf moved back to Germany as professor at the
Technical University of Munich. Since 2011 Ralf has been chair professor for
Theoretical Physics at Potsdam University. From 2009 until 2014 Ralf is also a
Finland Distinguished Professor at Tampere University of Technology, Finland.
Scientifically, Ralf is a statistical mechanician working on stochastic
processes and biological physics processes. In particular Ralf has been one of
the promoters of fractional dynamic equations in physics.
Awards:
-MINERVA Amos de Shalit fellow
-Alexander von Humboldt Feodor Lynen fellow
-DFG Emmy Noether I fellow
-Finland Distinguished Professor
Research topics:
-The statistical and nonequilibrium behaviour of
biopolymers, such as DNA/RNA, proteins and enzymes, and their
interactions. This includes the study of the denaturation transition of
double-stranded DNA, in particular under the influence of an external,
longitudinal pulling force. Investigating the dynamics of localized,
intermittent denaturation zones, and their interactions with the (un)binding
dynamics of proteins that specifically bind to single-stranded DNA. Developing
models to combine the mechanisms involved in gene regulation both in vitro
and in vivo.
-Generic aspects of search
strategies, in particular, the effect of scale-free search
mechanisms. These provide searching agents with a means to escape the central
limit theorem and avoid oversampling, which is the major shortcoming of Brownian
search strategies in one and two dimensions. In fact, search strategies
involving scale-free trajectories have been found in cases ranging from
facilitated diffusion in in vitro gene regulation, to the foraging behaviour of
bacteria and spider monkeys.
-Anomalous stochastic processes, such as Lévy flights and
subdiffusion. This research involves collaboration with experimental
groups using single molecule fluorescence, optical tweezers, and atomic force
microscopy. We also collaborate with a number of theoretical groups in several
countries.
Selected Papers:
1. Sandev
Trifce; Metzler Ralf; Tomovski Zivorad, Fractional diffusion equation with a
generalized Riemann-Liouville time fractional derivative, JOURNAL OF PHYSICS
A-MATHEMATICAL AND THEORETICAL, Vol. 44, No. 25, 2011
2. Tejedor V.; Benichou O.; Metzler Ralf; et al., Residual mean
first-passage time for jump processes: theory and applications to Levy flights
and fractional Brownian motion, JOURNAL OF PHYSICS A-MATHEMATICAL AND
THEORETICAL, Vol. 44, No. 25, 2011
3. Burov Stas; Jeon Jae-Hyung; Metzler Ralf; et al., Single particle tracking in
systems showing anomalous diffusion: the role of weak ergodicity breaking,
PHYSICAL CHEMISTRY CHEMICAL PHYSICS, Vol. 13, No. 5, 2011
4. Jeon Jae-Hyung; Metzler Ralf, Analysis of short subdiffusive time
series: scatter of the time-averaged mean-squared displacement, JOURNAL OF
PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol. 43, No. 25, 2010
5. Cottone Giulio; Di Paola Mario; Metzler Ralf, Fractional calculus
approach to the statistical characterization of random variables and vectors,
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, Vol. 389, No. 5, 2010
6. Jeon Jae-Hyung; Metzler Ralf, Fractional Brownian motion and motion
governed by the fractional Langevin equation in confined geometries, PHYSICAL
REVIEW E, Vol. 81, No. 2, 2010
7. Zaid Irwin M.; Lomholt Michael A.; Metzler Ralf, How Subdiffusion
Changes the Kinetics of Binding to a Surface, BIOPHYSICAL JOURNAL, Vol. 97, No.
3, 2009
8. Metzler Ralf; Chechkin Aleksei V.; Gonchar Vsevolod Yu.; et al., Some
fundamental aspects of Levy flights, Conference: Denton Workshop on In Search of
a Theory of Complexity held in Honor of Radu Balescu Location: Denton, TX Date:
AUG, 2005
CHAOS SOLITONS & FRACTALS, Vol. 34, No. 1, 2007
9. Lomholt Michael A.; Zaid Irwin M.; Metzler Ralf, Subdiffusion and weak
ergodicity breaking in the presence of a reactive boundary, PHYSICAL REVIEW
LETTERS, Vol. 98, No. 20, 2007
10. Chechkin Aleksei V.; Sliusarenko Oleksii Yu.; Metzler Ralf; et al.,
Barrier crossing driven by Levy noise: Universality and the role of noise
intensity, PHYSICAL REVIEW E, Vol. 75, No. 4, 2007
11. Metzler Ralf and Klafter Joseph. The restaurant at the end of
the random walk: recent developments in the description of anomalous transport
by fractional dynamics. J. Phys. A: Math. Gen. 37, R161 (2004).
doi:10.1088/0305-4470/37/31/R01.
12. Metzler Ralf; Klafter Joseph. The random walk's guide to
anomalous diffusion: a fractional dynamics approach, Physics Reports, 339 (1),
1–77 (2000).
13. Metzler Ralf, Barkai Eli, and Klafter Joseph. Anomalous
Diffusion and Relaxation Close to Thermal Equilibrium: A Fractional
Fokker-Planck Equation Approach. Phys. Rev. Lett. 82, 3563–3567 (1999).
==========================================================================
The End of This Issue
∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽