FDA Express Vol. 5, No. 6, Dec. 30, 2012
Editors:
W. Chen H.G. Sun
H. Wei
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
◆ Latest SCI Journal Papers on FDA
◆ Conferences
International Symposium on Fractional PDEs: Theory, Numerics and Applications
First Workshop on Fractional Calculus and Its Applications
◆ Books
Analytic Methods of Analysis and Differential Equations
◆ Journals
International Journal of Bifurcation and Chaos
◆ Paper Highlight
Multiple (multiindex) Mittag–Leffler functions and relations to generalized
fractional calculus
The fundamental solution of the space-time fractional diffusion equation
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Latest
SCI Journal Papers on FDA
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Title:
Numerical solution of nonlinear
fractional-order Volterra integro-differential equations by SCW
Author(s): Zhu, Li; Fan, Qibin
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18
Issue: 5 Pages: 1203-1213 DOI: 10.1016/j.cnsns.2012.09.024 Published:
MAY 2013
Title:
Bifurcation and resonance induced by
fractional-order damping and time delay feedback in a Duffing system
Author(s): Yang, J. H.; Zhu, H.
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18
Issue: 5 Pages: 1316-1326 DOI: 10.1016/j.cnsns.2012.09.023 Published:
MAY 2013
Title:
A continuous/discrete fractional Noether's
theorem
Author(s): Bourdin, Loic; Cresson, Jacky; Greff, Isabelle
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18
Issue: 4 Pages: 878-887 DOI: 10.1016/j.cnsns.2012.09.003 Published: APR
2013
Title:
Fractional variational integrators for
fractional Euler-Lagrange equations with holonomic constraints
Author(s): Wang, Dongling; Xiao, Aiguo
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18
Issue: 4 Pages: 905-914 DOI: 10.1016/j.cnsns.2012.08.025 Published: APR
2013
Title:
Existence of a weak solution for fractional
Euler-Lagrange equations
Author(s): Bourdin, Loic
Source: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: 399 Issue:
1 Pages: 239-251 DOI: 10.1016/j.jmaa.2012.10.008 Published: MAR 1 2013
Title:
Generalized transversality conditions in
fractional calculus of variations
Author(s): Almeida, Ricardo; Malinowska, Agnieszka B.
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18
Issue: 3 Pages: 443-452 DOI: 10.1016/j.cnsns.2012.07.009 Published: MAR
2013
Title:
Synchronization of integer order and
fractional order Chua's systems using robust observer
Author(s): El Gammoudi, Ichraf; Feki, Moez
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18
Issue: 3 Pages: 625-638 DOI: 10.1016/j.cnsns.2012.08.005 Published: MAR
2013
Title:
Renewal processes based on generalized
Mittag-Leffler waiting times
Author(s): Cahoy, Dexter O.; Polito, Federico
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18
Issue: 3 Pages: 639-650 DOI: 10.1016/j.cnsns.2012.08.013 Published: MAR
2013
Title:
Comment on "Parameter identification and
synchronization of fractional-order chaotic systems" [Commun Nonlinear Sci Numer
Simulat 2012; 17: 305-16]
Author(s): Jafari, Sajad; Golpayegani, S. M. Reza H.; Darabad, Mansour R.
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18
Issue: 3 Pages: 811-814 DOI: 10.1016/j.cnsns.2012.07.020 Published: MAR
2013
Title:
Remarks on the "Reply to Comments on "Fuzzy
fractional order sliding mode controller for nonlinear systems, Commun Nonlinear
Sci Numer Simulat 15 (2010) 963-978""
Author(s): Aghababa, Mohammad Pourmahmood
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18
Issue: 3 Pages: 815-818 DOI: 10.1016/j.cnsns.2012.07.026 Published: MAR
2013
Title:
Existence and uniqueness of
mild solution for an impulsive neutral fractional integro-differential equation
with infinite delay
Author(s): Dabas, Jaydev; Chauhan,
Archana
Source: MATHEMATICAL AND COMPUTER MODELLING Volume: 57 Issue: 3-4 Pages:
754-763 DOI: 10.1016/j.mcm.2012.09.001 Published: FEB 2013
Title:
On stability of difference
schemes in fractional spaces
Author(s): Ashyralyev, Allaberen;
Batyrov, Ahmet
Source: MATHEMATICAL AND COMPUTER
MODELLING Volume: 57 Issue: 3-4 Pages: 900-908 DOI:
10.1016/j.mcm.2012.09.017 Published: FEB 2013
Title:
Acoustic propagation in
viscous fluid with uniform flow and a novel design methodology for ultrasonic
flow meter
Author(s): Chen, Yong; Huang, Yiyong; Chen, Xiaoqian
Source: ULTRASONICS Volume: 53 Issue: 2 Pages: 595-606 DOI:
10.1016/j.ultras.2012.10.005 Published: FEB 2013
Title:
Stability of q-fractional
non-autonomous systems
Author(s): Jarad, Fahd; Abdeljawad, Thabet; Baleanu, Dumitru
Source: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS Volume: 14 Issue: 1
Pages: 780-784 DOI: 10.1016/j.nonrwa.2012.08.001 Published: FEB
2013
Title:
Nonexistence of periodic
solutions and asymptotically periodic solutions for fractional differential
equations
Author(s): Wang, JinRong; Feckan, Michal; Zhou, Yong
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18
Issue: 2 Pages: 246-256 DOI: 10.1016/j.cnsns.2012.07.004 Published: FEB
2013
Title:
Fractional generalization of
memristor and higher order elements
Author(s): Tenreiro Machado, J.
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18
Issue: 2 Pages: 264-275 DOI: 10.1016/j.cnsns.2012.07.014 Published: FEB
2013
Title:
Spread spectrum
communication and its circuit implementation using fractional-order chaotic
system via a single driving variable
Author(s): Cao, Hefei; Zhang, Ruoxun; Yan, Fengli
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 18
Issue: 2 Pages: 341-350 DOI: 10.1016/j.cnsns.2012.06.027 Published: FEB
2013
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Conferences
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
International Symposium on Fractional PDEs: Theory, Numerics and Applications
June 3 - 5, 2013, Salve Regina University, 100 Ochre Point Avenue, Newport RI 02840
Conference Objectives
Fractional Partial Differential Equations (FPDEs) are emerging as a new
powerful tool for modeling the most difficult type of complex systems, i.e.,
systems with overlapping microscopic and macroscopic scales or systems with
long-range time memory and long-range spatial interactions. They offer a new way
of accessing the mesoscale using the continuum formulation and hence extending
the continuum description for multiscale modeling of viscoelastic materials,
control of autonomous vehicles, transitional and turbulent flows, wave
propagation in porous media, electric transmission lines, and speech signals.
The aim of this first workshop in the USA on FPDEs is to cover theory,
algorithms and applications. Recent activity on FPDEs has taken place mostly in
China and to a lesser degree in Europe; hence we have invited our overseas
colleagues to share with US researchers the new advances in the methodology and
applications of FPDEs. We also expect many young US postdocs to attend the
workshop, hence introducing the new generation of simulation scientists to these
emerging computational methods.
Organizing Committee
George Em Karniadakis and Jan Hesthaven, Brown University, Organizers
Ernest Rothman, Salve Regina University, Local Organizer
Ms. Madeline Brewster, Madeline_Brewster@Brown.edu, 401. 863.1414, Contact
Scientific Commitee
Wen Chen Hohai University, China
Kai Diethelm University of Chester, United Kingdom
Fawang Liu Queensland University of Technology, Australia
Francesco Mainardi University of Bologna, Italy
Mark Meerschaaert Michigan State University, USA
Igor Podlubny Technical University of Kosice, Slovak Republic
Zhizhong Sun Southeast University, China
Bruce West Duke University, USA
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First Workshop on Fractional Calculus and Its Applications
April 25-26, 2013, Al-Ain,
United Arab Emirates
http://www.cos.uaeu.ac.ae/department/mathematical/conferences/workshop2013/
The Department of Mathematical Sciences at the United Arab Emirates University is proud to organize the First Workshop on Fractional Calculus and Its Applications. This international workshop aims to bring together academicians, researchers and scientists for knowledge sharing in the field of fractional calculus and serves as a good platform for researchers to meet and exchange ideas. The workshop will be held on Thursday and Friday, April 25-26, 2013, and it will be followed by the UAE Mathday Conference on 27 April, 2013, see at http://www.cos.uaeu.ac.ae/department/mathematical/conferences/uae math day 2013/, and it is possible (but not required) to take part in both events.
Objectives:
1- To present the most recent results in the field of fractional calculus.
2- To present and identify interesting applications of fractional differential
equations.
3- To serve as a platform for knowledge and information exchange between the
experts in the field.
4- To identify potential collaboration among the participants.
More details and current information: visit the Workshop website
Deadlines:
The deadline for submitting the registration form (online at the website) is
February 15, 2013.
For contacts:
Dr. Mohammed Al-Refai, Email: Malrefai@uaeu.ac.ae;
Reported by Yury Luchko, Email: luchko@beuth-hochschule.de
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Analytic Methods of Analysis and Differential Equations
Sergei V. Rogosin (Editor)
The book contains selected papers based on the plenary lectures presented at the 5th International Conference “Analytic Methods of Analysis and Differential Equations” (AMADE-2009) (14-19 Sept., 2009, Minsk, Belarus). Key topics of the Conference were integral transforms and special functions, differential equations, integral, difference, functional equations and fractional calculus, real and complex analysis, applied questions of analysis and differential equations, modern problems of mechanics.
It was the last AMADE Conference headed by Professor Anatoly Kilbas (1948-2010). This book is dedicated to his memory. It contains, in particular, two contributions by A. Kilbas and a series of his latest photos.
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Sergei V. Rogosin, Anna A. Koroleva (Editors)
This book contains survey papers based on the lectures presented at the 3rd International Winter School “Modern Problems of Mathematics and Mechanics” held in Jan. 2010 at Belarusian State University (BSU), Minsk and initiated by the Council of Young Scientists of BSU. Young researches, graduate, master and post-graduate students from Belarus, Lithuania, Poland and Ukraine participated in this school.
The lectures were devoted to different problems of modern analysis and its applications and among the lecturers were well-known experts in these topics. An extended presentation of modern problems of applied analysis enables the reader to get familiar with new approaches of mostly interdisciplinarycharacter. The results discussed are application oriented and present new insight into problems of growing importance such as applications to composite materials, anomalous diffusion, and fluid dynamics.
A cycle of lectures by V. Kisil (Leeds Univ., UK), “Erlangen program at large: A brief outline” describes a bridge between modern analysis and algebra. The author studies objects and properties, which are invariant under a group action. He starts with conformal geometry and develops a special functional calculus. As a characteristic example it is used the construction of wavelets basing on certain algebraic technique.
A. Laurincikas (Vilnius Univ., Lithuania), in his cycle “The Riemann zeta-function: Approximation of analytic functions”, deals with the notion of universality of functions. He shows that one of the best candidate to be universal is the classical Riemann zeta-function. So this lecture can be considered as describing connection between Analysis and Number Theory.
A cycle of lectures by Yu. Luchko (Beuth Tech. Univ. of Appl. Sci. Berlin, Germany), “Anomalous diffusion: Models, their analysis, and interpretation” presents the model of anomalous diffusion. This model is given in terms of differential equations of an arbitrary order. The obtained equations and their generalizations are analyzed both with the help of the Laplace-Fourier transforms (the Cauchy problems) and the spectral method (initial-boundary-value problems).
V. Mityushev (Krakow Pedagogical Academy, Poland), in his cycle “R–linear and Riemann–Hilbert problems for multiply connected domains” presents elements of constructive analysis related to the solution of boundary value problems for analytic functions. Main attention is paid to further application of the obtained results in the theory of 2D composite materials and porous media.
Another type of applications are presented in the cycle of lectures by S. Plaksa (Institute of Math., National Acad. Sci., Ukraine), “Commutative algebras associated with classic equations of mathematical physics”. He develops a technique connected with application of the theory of monogenic functions in the modern problems of mathematical physics. In particular, axial-symmetric problems of the mechanics of continuous media are studied.
S. Rogosin (Belarusian State Univ., Belarus) describes modern ideas which are applied at the study of 2D free boundary problems (“2D free boundary value problems”). In particular, an illustrative example is developed dealing with so-called Hele-Shaw boundary value problem. This problem is reduced to the couple of problems, namely, an abstract Cauchy- Kovalevsky problem and Riemann-Hilbert-Poincare problem for analytic functions.
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Volume 22, Number 11 (November 2012)
Tutorials and Reviews
PHENOMENOLOGY OF RETAINED REFRACTORINESS: ON SEMI-MEMRISTIVE DISCRETE MEDIA
COMPLEX BEHAVIOR IN COUPLED CHAOTIC CIRCUITS RELATED BY INTERMITTENCY AND ITS
MODELING METHODS
YOKO UWATE, YOSHIFUMI
NISHIO
DETECTING STRETCH-AND-FOLD MECHANISM IN CHAOTIC DYNAMICS
YUTAKA SHIMADA, TAIJI
YAMADA, TOHRU
IKEGUCHI
EVOLUTIONARY STRATEGY DYNAMICS FOR TAG-BASED COOPERATION AND DEFECTION IN THE
SPATIAL AND ASPATIAL SNOWDRIFT GAME
ROBERT A. LAIRD
Papers
APPLYING COMBINATORIAL OPTIMIZATION HEURISTICS FOR ENHANCING THE PERFORMANCE OF
TH-PPM UWB SYSTEMS: CHAOTIC VERSUS CLASSICAL CODE SEQUENCES
ANIS NAANAA, SAFYA BELGHITH
SYNCHRONIZATION AS A PROCESS OF SHARING AND TRANSFERRING INFORMATION
ERIK M. BOLLT
AN UPPER BOUND OF THE DIRECTIONAL ENTROPY WITH RESPECT TO THE MARKOV MEASURES
HASAN AKIN
A BIQUADRATIC SYSTEM OF TWO ORDER ONE DIFFERENCE EQUATIONS: PERIODS, CHAOTIC
BEHAVIOR OF THE ASSOCIATED DYNAMICAL SYSTEM
GUY BASTIEN, MARC ROGALSKI
DESIGN AND CIRCUIT IMPLEMENTATION OF FRACTIONAL-ORDER MULTIWING CHAOTIC
ATTRACTORS
ZILONG TANG, CHAOXIA ZHANG, SIMIN YU
TRANSITION CURVES AND BIFURCATIONS OF A CLASS OF FRACTIONAL MATHIEU-TYPE
EQUATIONS
Y. T. LEUNG, ZHONGJIN GUO, H. X. YANG
BIFURCATION ANALYSIS OF SYNCHRONIZED REGIONS IN COMPLEX DYNAMICAL NETWORKS
LONGKUN TANG, JUN-AN LU, JINHU LÜ, XINGHUO YU
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Volume 46, In Progress (January 2013)
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Multiple (multiindex) Mittag–Leffler functions and relations to generalized fractional calculus
Publication information: Virginia S. Kiryakova. Multiple (multiindex) Mittag–Leffler functions and relations to generalized fractional calculus. Journal of Computational and Applied Mathematics, 118(1–2), 2000, 241–259.Abstract
The classical Mittag–Leffler (M–L) functions have already proved their
efficiency as solutions of fractional-order differential and integral equations
and thus have become important elements of the fractional calculus’ theory and
applications. In this paper we introduce analogues of these functions, depending
on two sets of multiple (m-tuple, m≥2
is an integer) indices. The hint for this comes from a paper by Dzrbashjan (Izv.
AN Arm. SSR 13 (3) (1960) 21–63) related to the case m=2. We study the
basic properties and the relations of the multiindex M–L functions with the
operators of the generalized fractional calculus. Corresponding generalized
operators of integration and differentiation of the so-called Gelfond–Leontiev-type,
as well as Borel–Laplace-type integral transforms, are also introduced and
studied.
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The fundamental solution of the space-time fractional diffusion equation
Francesco Mainardi, Yuri Luchko and Gianni Pagnini
Publication information: Francesco Mainardi, Yuri Luchko and Gianni Pagnini. The fundamental solution of the space-time fractional diffusion equation. Fractional Calculus and Applied Analysis, Vol. 4 No 2 (2001) 153-192.
Abstract
We deal with the Cauchy problem for the space-time fractional diffusion
equation, which is obtained from the standard diffusion equation by replacing
the second-order space derivative with a Riesz-Feller derivative of order
a∈
(0, 2] and skewness
q
(|q
| ≤ min {
a,
2 − a}),
and the first-order time derivative with a Caputo derivative of order
b∈
(0, 2]. The fundamental solution (Green function) for the Cauchy problem is
investigated with respect to its scaling and similarity properties, starting
from its Fourier-Laplace representation. We review the particular cases of
space-fractional diffusion {0 <
a
≤ 2, b
= 1}, time-fractional diffusion {
a
= 2, 0 <
b
≤ 2}, and neutral-fractional diffusion {0 <
a
=b
≤ 2} , for which the fundamental solution can be interpreted as a spatial
probability density function evolving in time. Then, by using the Mellin
transform, we provide a general representation of the Green functions in terms
of Mellin-Barnes integrals in the complex plane, which allows us to extend the
probability interpretation to the ranges {0 <
a
≤ 2}∩{0 <
b
≤ 1} and {1 <
b
≤ a
≤ 2}. Furthermore, from this representation we derive explicit formulae
(convergent series and asymptotic expansions), which enable us to plot the
spatial probability densities for different values of the relevant parameters
a,
q,
b.
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The End of This Issue
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