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

Title: Fractional Voronovskaya type asymptotic expansions for bell and squashing type neural network operators
Author(s): Anastassiou, George A.
Source: JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS Volume: 15 Issue: 7 Pages: 1231-1239 Published: NOV 2013

Title: Two compartmental fractional derivative model with fractional derivatives of different order
Author(s): Popovic, Jovan K.; Pilipovic, Stevan; Atanackovic, Teodor M.
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18 Issue: 9 Pages: 2507-2514 DOI: 10.1016/j.cnsns.2013.01.004 Published: SEP 2013

Title: Lipschitz type smoothness of the fractional integral on variable exponent spaces
Author(s): Ramseyer, M.; Salinas, O.; Viviani, B.
Source: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: 403 Issue: 1 Pages: 95-106 DOI: 10.1016/j.jmaa.2012.12.074 Published: JUL 1 2013

Title: Two regularization methods to identify a space-dependent source for the time-fractional diffusion equation
Author(s): Wang, Jun-Gang; Zhou, Yu-Bin; Wei, Ting
Source: APPLIED NUMERICAL MATHEMATICS Volume: 68 Pages: 39-57 DOI: 10.1016/j.apnum.2013.01.001 Published: JUN 2013

Title: Riesz transforms, fractional power and functional calculus of Schrodinger operators on weighted L-p-spaces
Author(s): Assaad, Joyce
Source: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: 402 Issue: 1 Pages: 220-233 DOI: 10.1016/j.jmaa.2013.01.024 Published: JUN 1 2013

[Back]

==========================================================================

Conferences

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

Call for papers: BCAM Workshop

------BCAM-Basque Center for Applied Mathematics in Bilbao (Basque Country - Spain), from November 6th to November 8th 2013
------On the occasion of the retirement of Francesco Mainardi
https://sites.google.com/site/fcpnlo/ or http://www.bcamath.org/en/activities/workshops

(Contributed by Prof. Francesco Mainardi)

Dear All:
We would like to invite you to submit a one-page abstract for oral or poster communication to the following workshop: Fractional Calculus, Probability and Non-local Operators: Applications and Recent Developments https://sites.google.com/site/fcpnlo/, http://www.bcamath.org/en/activities/workshops
The workshop will be held at BCAM-Basque Center for Applied Mathematics in Bilbao (Basque Country - Spain), from November 6th to November 8th 2013, on the occasion of the retirement of Francesco Mainardi.
Non-exhaustive list of topics
Non-local operators and other mathematical tools generalizing classical methods,
Modeling of anomalous diffusion and relaxation,
Fractional calculus in applied sciences,
Related probability topics (random walks, Levy processes, Feller processes) and their applications.

We welcome contributions in the spirit of Problems-for-Solutions/Solutions-for-Problems.

The abstracts will be reviewed and ranked by the Scientific Committee. Selected full length papers will be published in a special issue of the peer-reviewed international journal: "Communications in Applied and Industrial Mathematics" http://caim.simai.eu/index.php/caim published by SIMAI (the Italian Society for Applied and Industrial Mathematics).

With the aim of offering you a valuable opportunity to showcase and disseminate your research, we would like to thank you in advance for your scientific contribution to the workshop.

FURTHER INFORMATION

Workshop e-mail: fcpnlo@gmail.com
Workshop Topics: https://sites.google.com/site/fcpnlo/topics
Details on abstract submission:
https://sites.google.com/site/fcpnlo/submissions

Participation fees:
Students: 50 euros, Regular participants: 100 euros. The fee will be paid directly at the registration desk in cash upon arrival at the conference site.
Important Dates
Abstract submission: by 31 June 2013
Notification of acceptance: by 31 July 2013
Full length paper submission deadline: by 31 January 2014

Invited Speakers:
Francesco Mainardi (Bologna University, IT),
Luisa Beghin (La Sapienza Rome University, IT),
Michele Caputo (La Sapienza Rome University, IT), and Texas A&M University, USA),
Rudolf Gorenflo (Berlin Free University, DE),
Jozsef Lorinczi (Loughborough University, UK),
Yuri Luchko (Berlin Beuth University, DE),
Mark M. Meerschaert (Michigan State University, USA)

Scientific Committee:
Michele Caputo (La Sapienza Rome University, IT, and Texas A&M University, USA),
Rudolf Gorenflo (Berlin Free University, DE),
Jozsef Lorinczi (Loughborough University, UK),
Yuri Luchko (Berlin Beuth University, DE),
Francesco Mainardi (Bologna University, IT),
Mark M. Meerschaert (Michigan State University, USA),
Gianni Pagnini (BCAM and IKERBASQUE, ES),
Enrico Scalas (East Piedmont University, IT, and BCAM, ES)

OrganizingCommittee:
Gianni Pagnini (BCAM and IKERBASQUE, ES),
Enrico Scalas (East Piedmont University, IT, and BCAM, ES)

Yours sincerely,

Gianni Pagnini
Enrico Scalas
Basque Center for Applied Mathematics Mazarredo 14, 48009 Bilbao, Basque Country, Spain
Tel. +34 946 567 842
www.bcamath.org
(matematika mugaz bestalde )

[Back]

==========================================================================
Books

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

Long-Memory Processes: Probabilistic Properties and Statistical Methods

Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik

Book Description
Long-memory processes are known to play an important part in many areas of science and technology, including physics, geophysics, hydrology, telecommunications, economics, finance, climatology, and network engineering. In the last 20 years enormous progress has been made in understanding the probabilistic foundations and statistical principles of such processes. This book provides a timely and comprehensive review, including a thorough discussion of mathematical and probabilistic foundations and statistical methods, emphasizing their practical motivation and mathematical justification. Proofs of the main theorems are provided and data examples illustrate practical aspects. This book will be a valuable resource for researchers and graduate students in statistics, mathematics, econometrics and other quantitative areas, as well as for practitioners and applied researchers who need to analyze data in which long memory, power laws, self-similar scaling or fractal properties are relevant.

Contents
1 Definition of Long Memory
2 Origins and Generation of Long Memory
3 Mathematical Concepts
4 Limit Theorems
5 Statistical Inference for Stationary Processes
6 Statistical Inference for Nonlinear Processes
7 Statistical Inference for Nonstationary Processes
8 Forecasting
9 Spatial and Space-Time Processes
10 Resampling
Appendix A Function Spaces
Appendix B Regularly Varying Functions
Appendix C Vague Convergence
Appendix D Some Useful Integral

[Back]

==========================================================================
Journals

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

Fractional Calculus and Applied Analysis

Volume: 16 Issue: 2
(From WEB OF KNOWLEDGE)

A note on Riesz fractional integrals in the limiting case alpha(x)p(x) a parts per thousand n
Samko, Stefan

What Euler could further write, or the unnoticed "big bang" of the fractional calculus
Podlubny, Igor

A numerical method for the fractional Schrodinger type equation of spatial dimension two
Ford, Neville J.; Manuela Rodrigues, M.; Vieira, Nelson

Time-fractional heat conduction in an infinite medium with a spherical hole under robin boundary condition
Povstenko, Yuriy

Representation of holomorphic functions by schlomilch's series
Rusev, Peter

Fractional operators in the matrix variate case
Mathai, A. M.; Haubold, Hans J.

Multi-parametric mittag-leffler functions and their extension
Kilbas, Anatoly A.; Koroleva, Anna A.; Rogosin, Sergei V.

Science metrics on fractional calculus development since 1966
Tenreiro Machado, J.; Galhano, Alexandra M.; Trujillo, Juan J.

The M-Wright function as a generalization of the Gaussian density for fractional diffusion processes
Pagnini, Gianni

Random numbers from the tails of probability distributions using the transformation method
Daniel Fulger, Enrico Scalas, Guido Germano

The mellin integral transform in fractional calculus
Luchko, Yuri; Kiryakova, Virginia

Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density
Gorenflo, Rudolf; Luchko, Yuri; Stojanovic, Mirjana

Almost sure and moment stability properties of fractional order Black-Scholes model
Zeng, Caibin; Chen, YangQuan; Yang, Qigui

[Back]

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

International Journal of Bifurcation and Chaos

Volume 23, Number 04

Feature Articles
CANARDS FROM CHUA'S CIRCUIT
JEAN-MARC GINOUX, JAUME LLIBRE, LEON O. CHUA

A GALLERY OF LORENZ-LIKE AND CHEN-LIKE ATTRACTORS
XIONG WANG, GUANRONG CHEN

COMPLETE PERIODICITY ANALYSIS FOR A DISCONTINUOUS RECURRENCE EQUATION
YEN CHIH CHANG, SUI SUN CHENG

Papers
SYNCHRONIZATION ANALYSIS FOR MULTIVALUED LOGICAL NETWORKS
FANGFEI LI, JITAO SUN

2D ELEMENTARY CELLULAR AUTOMATA WITH FOUR NEIGHBORS
JOSÉ ANTÓNIO FREITAS, RICARDO SEVERINO

INTEGRABILITY AND BIFURCATIONS OF LIMIT CYCLES IN A CUBIC KOLMOGOROV SYSTEM
FENG LI

COMPLEX DYNAMICS AND FAST-SLOW SCALE INSTABILITY IN CURRENT-MODE CONTROLLED BUCK CONVERTER WITH CONSTANT CURRENT LOAD
GUOHUA ZHOU, BOCHENG BAO, JIANPING XU

ESTIMATING THE UNCERTAINTY OF THE BEHAVIOR OF A PWM POWER CONVERTER BY ANALYZING A SET OF EXPERIMENTAL BIFURCATION DIAGRAMS
YURY KOLOKOLOV, ANNA MONOVSKAYA

NUMBER OF LIMIT CYCLES OF SOME POLYNOMIAL LIÉNARD SYSTEMS
WEIJIAO XU, CUIPING LI

DETECTING THE STATE OF THE DUFFING OSCILLATOR BY PHASE SPACE TRAJECTORY AUTOCORRELATION
VAHID RASHTCHI, MOHSEN NOURAZAR

LOWER BOUNDS FOR THE MAXIMUM NUMBER OF LIMIT CYCLES OF DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS WITH A STRAIGHT LINE OF SEPARATION
J. LLIBRE, M. A. TEIXEIRA, J. TORREGROSA

BIFURCATIONS OF LIMIT CYCLES FOR A PERTURBED CUBIC SYSTEM WITH DOUBLE FIGURE EIGHT LOOP
TONGHUA ZHANG, HONG ZANG, MOSE O. TADE

PERIODICALLY PULSED IMMUNOTHERAPY IN A MATHEMATICAL MODEL OF TUMOR-IMMUNE INTERACTION
HSIU-CHUAN WEI, JENN-TSANN LIN

ON THE NUMBER AND DISTRIBUTIONS OF LIMIT CYCLES OF A PLANAR QUARTIC VECTOR FIELD
YUHAI WU, MAOAN HAN

STOCHASTIC POINCARÉ–BENDIXSON THEOREM AND ITS APPLICATION ON STOCHASTIC HOPF BIFURCATION
XIAOLING ZOU, KE WANG, DEJUN FAN

ON PERIODIC SOLUTIONS OF 2-PERIODIC LYNESS' EQUATIONS
GUY BASTIEN, VÍCTOR MAÑOSA, MARC ROGALSKI

A NUMERICAL STUDY OF UNIVERSALITY AND SELF-SIMILARITY IN SOME FAMILIES OF FORCED LOGISTIC MAPS
PAU RABASSA, ÀNGEL JORBA, JOAN CARLES TATJER

SIMPLE MEMRISTIVE TIME-DELAY CHAOTIC SYSTEMS
VIET-THANH PHAM, ARTURO BUSCARINO, LUIGI FORTUNA, MATTIA FRASCA

ESTIMATION OF CHAOTIC THRESHOLDS FOR THE RECENTLY PROPOSED ROTATING PENDULUM
N. HAN, Q. J. CAO, M. WIERCIGROCH

BREAKING A CHAOTIC IMAGE ENCRYPTION ALGORITHM BASED ON MODULO ADDITION AND XOR OPERATION
CHENGQING LI, YUANSHENG LIU, LEO YU ZHANG, MICHAEL Z. Q. CHEN

NETWORK SYNCHRONIZATION BY DYNAMIC DIFFUSIVE COUPLING
C. MURGUIA, R. H. B. FEY, H. NIJMEIJER

WAVE PROPAGATION FOR MONOSTABLE 2-D LATTICE DIFFERENTIAL EQUATIONS WITH DELAY
CUI-PING CHENG, YOU-HUI SU, ZHAOSHENG FENG

[Back]

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

Discontinuity, Nonlinearity, and Complexity

Volume 2, Issue 2 June 2013
https://lhscientificpublishing.com/Journals/DNC-Download.aspx
(Contributed by Tenreiro Machado)

Contents
Fractional Fourier Detection of Lévy Flights: Application to Hamiltonian Chaotic Trajectories
Françoise Briolle, Xavier Leoncini, and Benjamin Ricaud

Cosmic Evolution in Fractional Action Cosmology
Victor K. Shchigolev

High Degree Multivariate Fuzzy Approximation by Quasi-Interpolation Neural Network Operators
George A. Anastassiou

Conservation Laws in Thomas' Model of Ion Exchange in a Heterogeneous Solution
N.H. Ibragimov and Raisa Khamitova

Solvability Conditions for Some Systems of Nonlinear Non-Fredholm Elliptic Equations
Vitali Vougalter

Parameter Characteristics of Projective Synchronization of two Gyroscope Systems with Different Dynamical Behaviors
Fuhong Min and Albert C.J. Luo

Synchronization of Two Identical Restricted Planar Isosceles Three-Body-Problem and a Study on Possible Chaos Control
Ayub Khan and Rimpi Pal

[Back]

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

Journal of Applied Nonlinear Dynamics

Volume 2, Issue 2 June 2013
https://lhscientificpublishing.com/Journals/JAND-Download.aspx
(Contributed by Tenreiro Machado)

Contents
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

[Back]

========================================================================
Paper Highlight
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

Variable-order fractional derivatives and their numerical approximations

Duarte Valério, José Sá da Costa

Publication information: Duarte Valério, José Sá da Costa, Variable-order fractional derivatives and their numerical approximations, Signal Processing, 91(3), 2011, 470-483.
http://www.sciencedirect.com/science/article/pii/S0165168410001404

Abstract
This paper addresses the different possible definitions of variable-order derivatives and their numerical approximations; both approximations based upon the definitions and approximations consisting of non-linear transfer functions (in particular combining existing approximations of constant-order fractional derivatives, such as the Crone approximation, with fuzzy logic) are considered. There are different possible configurations, implementing variable-order fractional derivatives both with and without memory of past values of the time-dependent differentiation order.

[Back]

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term

P. Zhuang, F. Liu, V. Anh, I. Turner

Publication information: P. Zhuang, F. Liu, V. Anh, I. Turner, Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term. SIAM J. Numer. Anal., 47(3), 1760–1781. (22 pages).
http://epubs.siam.org/doi/abs/10.1137/080730597?journalCode=sjnaam

Abstract
In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moveover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.

[Back]

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

Finite difference schemes for variable-order time fractional diffusion equation

HongGuang Sun, Wen Chen, Changpin Li, YangQuan Chen

Publication information: HongGuang Sun, Wen Chen, Changpin Li, YangQuan Chen. Finite difference schemes for variable-order time fractional diffusion equation. International Journal of Bifurcation and Chaos (2012), 22 (4): 1250085 (16 pages).
http://www.worldscientific.com/doi/abs/10.1142/S021812741250085X

Abstract
Variable-order fractional diffusion equation model is a recently developed and promising approach to characterize time-dependent or concentration-dependent anomalous diffusion, or diffusion process in inhomogeneous porous media. To further study the properties of variable order time fractional subdiffusion equation models, the efficient numerical schemes are urgently needed. This paper investigates numerical schemes for variable-order time fractional diffusion equations in a finite domain. Three finite difference schemes including the explicit scheme, the implicit scheme and the Crank-Nicholson scheme are studied. Stability conditions for these three schemes are provided and proved via the Fourier method, rigorous convergence analysis is also performed. Two numerical examples are offered to verify the theoretical analysis of the above three schemes and illustrate the effectiveness of suggested schemes. The numerical results illustrate that, the implicit scheme and the Crank-Nicholson scheme can achieve high accuracy compared with the explicit scheme, and the Crank--Nicholson scheme claims highest accuracy in most situations. Moreover, some properties of variable-order time fractional diffusion equation model are also shown by numerical simulations.

[Back]

==========================================================================

The End of This Issue

∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽