FDA Express Vol. 2, No. 1, Jan. 15, 2012
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Editors:
W. Chen H.G. Sun
X.D. Zhang
S. Hu
Institute of Soft Matter Mechanics, Hohai University
For contribution:
fdaexpress@hhu.edu.cn
For subscription:
http://em.hhu.edu.cn/fda/subscription.htm
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бЇ Conferences
Update of the Fifth IFAC Symposium on Fractional Differentiation and its Applications (FDA12)
бЇBooks
Advances in Fractional Calculus
Fractional Calculus Models and Numerical Methods
бЇ Journals
Fractional Calculus and Applied Analysis
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Researchers & Groups
Jordan Research Group in Applied
Mathematics (JRGAM)
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Toolbox
Numerical Inversion of Laplace Transforms in Matlab
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Conferences
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Update of the Fifth IFAC Symposium on Fractional Differentiation and its Applications - FDA12
May
14-17 2012, Hohai University, Nanjing, China
Websiteг║http://em.hhu.edu.cn/fda12/
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Invitation to FDA12
The purpose of this Symposium in series is to provide the participants with a broad overview of the state of the art on fractional systems, leading to the cross-fertilization of new research on theoretical, experimental and computational fronts for potential uses of fractional differentiation in diverse applications. The organizing committee invites you from all over the world to come to Nanjing to attend this wonderful event.
Up to 14th January 2012, the organization committee has received 252 abstracts. Thanks for the contributions from our colleagues around the world! Because the original deadline of the abstract submission happens to be in the Christmas and New Year holidays, many colleagues have recently suggested to further extend the deadline. And the organization committee has thus decided to extend the abstract submission deadline to 31st January 2012. Please help inform our FDA colleagues, who have yet to submit his/her abstracts, do it as early as possible.
The FDA12 will be held from 14th-17th May 2012 in Nanjing, China. We are looking forward to meeting you at the FDA12. For details please visit http://em.hhu.edu.cn/fda12.
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New Books
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(J. Sabatier, O. P. Agrawal and J. A. Tenreiro Machado)
Fractional Calculus is a new growing field. Up to this point, researchers, scientists, and engineers have been reluctant to accept the fact that Fractional Calculus can be used in the analysis and design of many systems of practical interests, whereas in similar applications the traditional calculus either fails or provides poor solutions
Many engineers, scientists, and applied mathematicians are looking for books that can provide many applications of Fractional Calculus. This book will provide a partial solution to this problem. Since it covers recent applications of Fractional Calculus, it will be attractive to many engineers, scientists, and applied mathematicians
In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation.
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As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.
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Contents:
1. Analytical and Numerical Techniques:
l Three Classes of FDEs Amenable to Approximation Using a Galerkin Technique, by S. I Singh, A. Chatterjee;
l Enumeration of the Real Zeros of the Mittag-Leffler Function, by J W. Hanneken, D. M Vaught, B. N. Narahari Achar;
l The Caputo Fractional Derivative: Initialization Issues Relative to Fractional Differential Equations, by B. N. Narahari Achar, C. F. Lorenzo, T. T. Hartley;
l Comparison of Five Numerical Schemes for Fractional Differential Equations, by O. P. Agrawal, P. Kumar;
l Sub-Optimum H2 Pseudo-Rational Approximations to Fractional Order Linear Time Invariant Systems, by D. Xue, Y. Chen;
l Linear Differential Equations of Fractional Order, by B. Bonilla, M. Rivero, J.J. Trujillo;
l Riesz Potentials as Centred Derivatives, by M.D. Ortigueira.
2. Classical Mechanics and Particle Physics:
l On Fractional Variational Principles, by D. Baleanu, S. Muslih;
l Fractional Kinetics In Pseudochaotic Systems And Its Applications, by G. M Zaslavsky;
l Semi-Integrals and Semi-Derivatives in Particle Physics, by P. W. Krempl;
l Mesoscopic Fractional Kinetic Equations versus a Riemarin-Liouville Integral Type, by R. R. Nigmatullin, J.J. Trujillo.
3. Diffusive Systems:
l Enhanced Yracer Diffusion in Porous Media with an Impermeable Boundary, by N. Krepysheva, L. Di Pietro, M C. Nижel;
l Solute Spreding in Heterogeneous Aggregated Porous Media, by K. Logvinova, M C. Nижel;
l Fractional Advective-Dispersive Equation as a Model of Solute Transport in Porous Media, by F. San Jose Martinez, Pachepsky, W. Rawls;
l Modelling and Identification of Diffusive Systems using Fractional Models, by A. Benchellal, T. Poinot, C. Trigeassou.
4 . Modeling:
l Identification of Fractional Models from Frequency Data, by D. Valижrio, I Sив da Costa;
l Dynamic Response of the Fractional Relaxor-Oscillator to a Harmonic Driving Force, by B. N. Narahari Achar, J.W. Hanneken;
l A Direct Approximation of Fractional Cole-Cole-Systems by Ordinary First Order Processes, by M Haschka, V. Krebs;
l Fractional Multi-Models of the Gastrocnemius Muscle for Tetanus Pattern, by L. Sommacal, P. Meichior, I M Cabelguen, A. Oustaloup, A. I Jspeert;
l Limited-Bandwidth Fractional Differentiator: Synthesis and Application in Vibration Isolation, by P. Serrier, X Moreau, A. Oustaloup.
5. Electrical Systems:
l A Fractional Calculus Perspective in the Evolutionary Design of Combinational Circuits, by C. Reis, J A. Tenreiro Machado, I B. Cunha;
l Electrical Skin Phenomena: A Fractional Calculus Analysis, by J. A. Tenreiro Machado, I S. Jesus, A. Gaihano, I B. Cunha, I K Tar;
l Implementation of Fractional-Order Operators on Field Programmable GateArrays, by C. X Jiang, J E. Carletta, T. T. Hartley;
l Complex Order-Distributions Using Conjugated-Order Differintegrals, by I L. Adams, Hartley, C. F. Lorenzo.
6. Viscoelastic and Disordered Media:
l Fractional Derivative Consideration on Nonlinear Viscoelastic Statical and Dynamical Behavior under Large Pre-displacement, by H. Nasuno, N. Shimizu, M Fukunaga;
l Quasi-Fractals: New Possibilities in Description of Disordered Media, by R. R. Nigmatullin, A. P. Alechin
l Fractional Damping: Stochastic Origin, and Finite Approximations, by S. J. Singh, A. Chatterjee; Analytical Modeling and Experimental Identification of Viscoelastic Mechanical Systems, by G. Catania, S. Sorrentino.
7. Control:
l LMI Characterization ofFractional Systems Stability, by M Moze, J. Sabatier, A. Oustaloup;
l Active Wave Control for Flexible Structures Using Fractional Calculus, by M Kuroda;
l Fractional Order Control of a Flexible Manipulator, by V. Feliu, B.M. Vinagre, C.A. Monje;
l Tuning-Rules for Fractional PIDs, by D. Valижrio, I Sив da Costa;
l Frequency Band-Limited Fractional Differentiator Prefilter in Path Tracking Design, by P. Melchior, A. Poty, A. Oustaloup;
l Flatness Control of a Fractional Thermal System, by P. Melchior, M Cugnet, I. Sabatier, A. Poty, A. Oustaloup;
l Robustness Comparison of Smith Predictor Based Control and Fractional-Order Control, by P. Lanusse, A. Oustaloup;
l Robust Design of an Anti-Windup Compensated 3rd Generation CRONE Controller, by P. Lanusse, A. Oustaloup, I. Sabatier;
l Robustness of Fractional Order Boundary Control of Time-Fractional Wave Equations with Delayed Boundary Measurement Using the Smith Predictor, by I Liang, W Zhang, Y. Chen, L Podlubny.
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---Series on Complexity, Nonlinearity and Chaos
(Dumitru Baleanu, Kai Diethelm, Enrico Scalas and Juan J Trujillo)
https://www.worldscibooks.com/mathematics/8180.html
The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering. These operators have been used to model problems with anomalous dynamics, however, they also are an effective tool as filters and controllers, and they can be applied to write complicated functions in terms of fractional integrals or derivatives of elementary functions, and so on.
This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models.
All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book was written with a trade-off in mind between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. Numerical code is also provided.
Contents:
Readership:
Undergraduate and graduate students, researchers and professionals in applied mathematics, analysis & differential equations and probability & statistics.
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Journals
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Volume 45, Issue 2 (February 2012)
Stochastic
growth of radial clusters: Weak convergence to the asymptotic profile and
implications for morphogenesis
Carlos Escudero
Fractal dimension evolution and spatial replacement dynamics of urban growth
Yanguang Chen
Negative correlation between power-law scaling and Hurst exponents in long-range
connective sandpile models and real seismicity
Ya-Ting Lee, Chien-chih Chen, Chai-Yu Lin, Sung-Ching Chi
Ordered chaotic bursting and multiple coherence resonance by time-periodic
coupling strength in NewmanиCWatts neuronal networks
Li Wang, Yubing Gong, Xiu Lin
Mixed quantization dimensions of self-similar measures
Meifeng Dai, Xiaoli Wang, Dandan Chen
Rational integrability of a nonlinear finance system
Claudia Valls
Finite-size effect and the components of multifractality in financial volatility
Wei-Xing Zhou
Maps serving the combined coupling for use in environmental models and their
behaviour in the presence of dynamical noise
Dragutin T. Mihailović, Mirko Budinčević, Dušanka Perišić, Igor Balaž
Minimizing the trend effect on detrended cross-correlation analysis with
empirical mode decomposition
Xiaojun Zhao, Pengjian Shang, Chuang Zhao, Jing Wang, Rui Tao
Dynamics of chaotic maps for modelling the multifractal spectrum of human brain
Diffusion Tensor Images
A. Provata, P. Katsaloulis, D.A. Verganelakis
Anomalous fractal dimension and GinzburgиCLandau phase transition study in high
energy nuclear interaction
Dipak Ghosh, Argha Deb, Ruma Saha, Rupa Das, Nurul Alam
From Heisenberg ansatz to attractor of Thirring Instanton
Beyrul Canbaz, Cem Onem, Fatma Aydogmus, K. Gediz Akdeniz
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Volume 14, Number 4 (2011)
Editorial:
FCAA news: Meetings and books
Articles:
Positive solutions for a semipositone fractional boundary value problem with a forcing term
On some inversion formulas for Riesz potentials and k-plane transforms
On the existence of solutions of fractional integro-differential equations
Impulse response of a generalized fractional second order filter
Erdижlyi-Kober fractional diffusion
On an equation being a fractional differential equation with respect to time and a pseudo-differential equation with respect to space related to Lижvy-type processes
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation
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Researchers & Groups
гнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгнгн
Website: http://www.mutah.edu.jo/jrgam/index.html
Applied Mathematics uses powerful mathematical tools to solve real-world problems, aided by state-of-the-art of computer facilities. In the Jordan Research Group in Applied Mathematics, they focus on the numerical solution of differential and integral equations, fractional calculus, mathematical physics, mathematical biology, fluid mechanics, mathematical modelling and financial mathematics.
Professor Shaher Momani (Coordinator
and Founder of the Group),
Research Interests:
Fractional Equations, Ordinary and Partial Differential Equation, Boundary Value
Problems, Non-Newtonian Fluid Mechanics, Linear and Nonlinear Dynamical Systems.
(Professor Shaher Momani is
One of the Top Ten Scientists in the World in Fractional Equations)
http://www.ju.edu.jo/faculties/facultyofscience/Mathematics/DepartmentStaff/Disp_Form.aspx?ID=55
Professor Ahmed D. Alawneh (Honorary Fellow), E-mail: alawneh@sci.ju.edu.jo, Research Interests: Ordinary and Partial Differential Equation, Boundary Value Problems, Fractional Calculus.
Professor Nabil T. Shawagfeh (Honorary Fellow), E-mail: shawagnt@ju.edu.jo, Research Interests: Ordinary BVP in Math. Physics, Differential Equations, Fractional Calculus, Special Functions.
Professor Muhammad Aslam Noor (Honorary Fellow) E-mail: noormaslam@hotmail.com & noormaslam@gmail.com, Research Interests: Numerical Analysis, Computing and Operations Research, variational inequalities theory, Numerical methods for variational inequalities.
Professor Abdul-Majid Wazwaz (Honorary Fellow), E-mail: wazwaz@sxu.edu, Research Interests: Solitary Wave Theory, PDEбпs, Numerical Analysis, Adomian Decomposition Method, Mathematical Physics.
Professor D. Baleanu (Honorary Fellow), E-mail: dumitru@cankaya.edu.tr, Research Interests: Fractional Calculus and its applications, Discrete Mathematics, Quantisation of the systems with constraints, Hamilton-Jacobi formalism, Geometries admitting generic and non-generic symmetries, The Wavelet method and its applications
Professor Samir Hadid, E-mail: sbhadid@yahoo.com,Research Interests: Fractional Calculus, Ordinary differential equations.
Professor Eqap M. Rabie, E-mail: eqap@mutah.edu.jo, Research Interests: Mathematical Physics.
Professor Khalida Inayat Noor, E-mail: Khalidanoor@hotmail.com, Research Interests: Geometric Function Theory and related topics, Functional Analysis and its applications in Numerical Analysis and Operations Research.
Dr. Zaid M. Odibat, Email: odibat@bau.edu.jo, Research Interests: Numerical Analysis, Ordinary and Partial defferential equations, Fractional Calculus.
Dr. Ishak Hashim, Email: ishak_h@ukm.my, Research Interests: Mathematical/Numerical methods, Fluid dynamics.
Dr. Shijun Liao, E-mail: sjliao@sjtu.edu.cn, Research Interests : Nonlinear Mechanics, Fluid Mechanics, Applied Mathematics.
Dr. Reyad El-Khazali, Email: khazali@ece.ac.ae, Research Interests: Non-Newtonian Fluid Mechanics, Nonlinear Waves, Fractional Calculus Linear and Nonlinear Dynamical Systems.
Dr. Vedat Erturk, (E-mail: vserturk@omu.edu.tr), Research Interests: Numerical Analysis, Ordinary and Partial defferential Equations.
Dr. Kamel M. Al-Khaled, (Email: kamel@just.edu.jo), Research Interests: Mathematical Modelling, Applied Differential Equations (Ordinary and Partial) and their numerical (or approximate) solutions using: Sinc Method, Adomian Decomposition Method, Tanh Method, variational iteration Method, Wavelets Method, Approximation Theory and Fractional Calculus.
Dr. Ameen J. Alawneh, (Email: ameen@just.edu.jo), Research Interests: Stochastic Processes, Queuing Systems, Simulation, Optimization, Financial Mathematics
Dr, Rabha W. Ibrahim, (E-mail: rabhaibrahim@yahoo.com), Research Interests: Differential and Integral Equations, Fractional Calculus, Set-Valued Functions.
Dr. Hossein Jafari, (E-mail: jafari@umz.ac.ir), Research Interests: Fractional Differential Equations, Integral Equations, Numerical Analysis, Iterative Methods.бб
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Toolbox
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by Juraj, 08 Sep 2011
(From Matlab Central)
Description
Inversion of Laplace transforms
is a very important procedure used in solution of complex linear systems. The
function f(t)=INVLAP(F(s)) offers a simple, effective and reasonably accurate
way to achieve the result. It is based on the paper: J. Valsa and L. Brancik:
Approximate Formulae for Numerical Inversion of Laplace Transforms, Int. Journal
of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 11,
(1998), pp. 153-166
The transform F(s) may be any reasonable function of complex variable s^ж┴, where
ж┴ is an integer or non-integer real exponent. Thus, the function INVLAP can
solve even fractional problems and invert functions F(s) containing rational,
irrational or transcendental expressions. The function does not require to
compute poles nor zeroes of F(s). It is based on values of F(s) for selected
complex values of the independent variable s. The resultant computational error
can be held arbitrarily low at the cost of CPU time. With the todayбпs computers
and their speed this does not present any serious limitation.
Download
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