FCAA related news, events and books (FCAA-Volume 19-2-2016)

1 Calendar of Events

Special Session on “Fractional Order Systems” in the Workshop Structural Dynamical Systems: Computational Aspects 2016 (SDS 2016), July 14–17, 2016

Hotel Villaggio Porto Giardino in Monopoli, Italy

Website:https://sites.google.com/site/workshopsds2016

The aim of the biennial workshop SDS: CA is to bring together researchers from different areas, in particular Mathematics, Physics and Engineering, to give them the opportunity of discussing in a friendly atmosphere, the recent developments in computational and theoretical methods for Dynamical Systems and their applications. The main topics are: – Continuous and Discrete Dynamical Systems; – Mathematical Models with Applications; – Piecewise-smooth Dynamical Systems and Discontinuous ODEs; – Numerical Methods for ODEs and PDEs; – Fractional Differential Equations; – Models and Simulation in Engineering Problems; numerical and theoretical aspects of these topics will be welcome.

Due to the great interest in systems with fractional integrals and derivatives, this year the topics of the workshop include also “Fractional Differential Equations” and a special issue devoted to “Fractional Order Systems” will be organized.

Your participation in this workshop and the presentation of a your work is highly welcome.

For more detailed information, contact:

Roberto Garrappa, E-mail: roberto.garrappa@uniba.it

2 New Books

Christopher Goodrich, Allan C. Peterson, Discrete Fractional Calculus. Ser. Mathematics – Dynamical Systems & Differential Equations, Springer (2015), 556 + xiii pp., ISBN: 978-3-319-25562-0.

Details at: http://www.springer.com/us/book/9783319255606.

About this book: This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the subject. Most chapters may be covered or omitted, depending upon the background of the student. For example, the text may be used as a primary reference in an introductory course for difference equations which also includes discrete fractional calculus. Chapters 1-2 provide a basic introduction to the delta calculus including fractional calculus on the set of integers. For courses where students already have background in elementary real analysis, Chapters 1-2 may be covered quickly and readers may then skip to Chapters 6-7 which present some basic results in fractional boundary value problems (FBVPs). Chapters 6-7 in conjunction with some of the current literature listed in the Bibliography can provide a basis for a seminar in the current theory of FBVPs. For a two-semester course, Chapters 1-5 may be covered in depth, providing a very thorough introduction to both the discrete fractional calculus as well as the integer-order calculus.

R.S. Stankovic, P.L. Butzer, F. Schipp, W.R. Wade, W. Su, Y. Endow, S. Fridli, B.I. Golubov, F. Pichler, Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science. Volume 1: Foundations. Ser. Atlantis Studies in Math. for Engineering and Science, Springer (2015), 455 + xxiv pp., ISBN 978-94-6239-160-4, A product of Atlantis Press.

Details at: http://www.springer.com/kr/book/9789462391598.

A monograph based on articles of the founding authors, reproduced in full. A unique development of a field by seven founding authors, together with reproductions of some of their basic papers. Applications to dyadic differential equations, approximation theory, etc. Reviews of former and recent results help the reader to get a fast introduction and a rather complete coverage of the area. A separate chapter with open problems should be useful for further research in the field

About this book: Dyadic (Walsh) analysis emerged as a new research area in applied mathematics and engineering in early seventies within attempts to provide answers to demands from practice related to application of spectral analysis of different classes of signals, including audio, video, sonar, and radar signals. In the meantime, it evolved in a mature mathematical discipline with fundamental results and important features providing basis for various applications. The book will provide fundamentals of the area through reprinting carefully selected earlier publications followed by overview of recent results concerning particular subjects in the area written by experts, most of them being founders of the field, and some of their followers. In this way, this first volume of the two volume book offers a rather complete coverage of the development of dyadic Walsh analysis, and provides a deep insight into its mathematical foundations necessary for consideration of generalizations and applications that are the subject of the second volume. The presented theory is quite sufficient to be a basis for further research in the subject area as well as to be applied in solving certain new problems or improving existing solutions for tasks in the areas which motivated development of the dyadic analysis.

R.S. Stankovic, P.L. Butzer, F. Schipp, W.R. Wade, W. Su, Y. Endow, S. Fridli, B.I. Golubov, F. Pichler, Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science. Volume 2: Extensions and Generalizations. Ser. Atlantis Studies in Math. for Engineering and Science # 13, Springer (2015), 360 + xviii pp., 9 illustr., ISBN 978-94-6239-162-8 (Print) 978-94-6239-163-5 (Online), A product of Atlantis Press.

Details at: http://www.springer.com/kr/book/9789462391598.

About this book: The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications. Considered are dyadic derivatives on Vilenkin groups and various other Abelian and finite non-Abelian groups. Since some important results were developed in former Soviet Union and China, we provide overviews of former work in these countries. Further, we present translations of three papers that were initially published in Chinese. The presentation continues with chapters written by experts in the area presenting discussions of applications of these results in specific tasks in the area of signal processing and system theory. Efficient computing of related differential operators on contemporary hardware, including graphics processing units, is also considered, which makes the methods and techniques of dyadic analysis and generalizations computationally feasible. The Volume 2 of the book ends with a chapter presenting open problems pointed out by several experts in the area.

Yong Zhou, Fractional Evolution Equations and Inclusions. Ser. Appl. Math., Elsevier (2016), 294 pp., ISBN 978-0-12-804277-9 (Print) 978-0-12-804775-0 (Electronic), Academic Press.

Details at: https://www.elsevier.com/books/fractional-evolution-equations-and-inclusions/unknown/978-0-12-804277-9, see also at: http://www.sciencedirect.com/science/book/9780128042779.

About this book: Fractional evolution inclusions are an important form of differential inclusions within nonlinear mathematical analysis. They are generalizations of the much more widely developed fractional evolution equations (such as time-fractional diffusion equations) seen through the lens of multivariate analysis. Compared to fractional evolution equations, research on the theory of fractional differential inclusions is however only in its initial stage of development.

This is important because differential models with the fractional derivative providing an excellent instrument for the description of memory and hereditary properties, and have recently been proved valuable tools in the modeling of many physical phenomena.

The fractional order models of real systems are always more adequate than the classical integer order models, since the description of some systems is more accurate when the fractional derivative is used. The advantages of fractional derivatization become evident in modeling mechanical and electrical properties of real materials, description of rheological properties of rocks and in various other fields. Such models are interesting for engineers and physicists as well as so-called pure mathematicians.

Phenomena investigated in hybrid systems with dry friction, processes of controlled heat transfer, obstacle problems and others can be described with the help of various differential inclusions, both linear and nonlinear.

Fractional Evolution Equations and Inclusions is devoted to a rapidly developing area of the research for fractional evolution equations and inclusions and their applications to control theory. It studies Cauchy problems for fractional evolution equations, and fractional evolution inclusions with Hille-Yosida operators. It discusses control problems for systems governed by fractional evolution equations. Finally it provides an investigation of fractional stochastic evolution inclusions in Hilbert spaces.

Key Features: – Systematic analysis of existence theory and topological structure of solution sets for fractional evolution inclusions and control systems; – Differential models with fractional derivative provide an excellent instrument for the description of memory and hereditary properties, and their description and working will provide valuable insights into the modelling of many physical phenomena suitable for engineers and physicists; – The book provides the necessary background material required to go further into the subject and explore the rich research literature.

Readership: Researchers and graduate students working in research, seminars, and advanced graduate courses in pure and applied mathematics, physics, mechanics, engineering, biology, and other applied sciences.

Claudia Bucur, Enrico Valdinoci, Nonlocal Diffusion and Applications. Ser. Lecture Notes of the Unione Mat. Italina # 20, Springer (2016), 155 pp. + xii, 3 b/w illust., 23 illustr in colour, ISBN 978-3-319-28739-3 (Print), ISBN 978-3-319-28738-6 (Electronic).

Details at: http://www.springer.com/us/book/9783319287386.

Gives a rich introduction to the fractional Laplacian and its applications Well explained, self-contained and easy to follow, even for those who are not familiar with the subject Contains brand new and interesting research trends on the fractional Laplacian.

About this book: Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given. Furthermore, an example of an s-harmonic function, its harmonic extension and some insight into a fractional version of a classical conjecture due to De Giorgi are presented. Although the aim is primarily to gather some introductory material concerning applications of the fractional Laplacian, some of the proofs and results are new. The work is entirely self-contained, and readers who wish to pursue related subjects of interest are invited to consult the rich bibliography for guidance.