Advanced Fractional Differential and Integral Equations
Authors: Said Abbas, Mouffak Benchohra and Gaston Mandata N’Guerekata
Morgan State University, MD, US |
Fractional calculus deals with extensions of derivatives and integrals to non-integer orders. It represents a powerful tool in applied mathematics to study a myriad of problems from di fferent fi elds of science and engineering, with many break-through results found in mathematical physics, fi nance, hydrology, biophysics, thermodynamics, control theory, statistical mechanics, astrophysics, cosmology and bioengineering. This book is devoted to the existence and uniqueness of solutions and some Ulam's type stability concepts for various classes of functional differential and integral equations of fractional order. Some equations present delay which may be fi nite, inf inite or state-dependent. Others are subject to multiple time delay e ffect. The tools used include classical fi xed point theorems. Other tools are based on the measure of non-compactness together with appropriates fi xed point theorems. Each chapter concludes with a section devoted to notes and bibliographical remarks and all the presented results are illustrated by examples. The content of the book is new and complements the existing literature in Fractional Calculus. It is useful for researchers and graduate students for research, seminars and advanced graduate courses, in pure and applied mathematics, engineering, biology and other applied sciences.
Review published in Zentralblatt MATH |
Advances in Linear Algebra Research
Editor: Ivan Kyrchei
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS of Ukraine To read additional reviews, click here.
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"This book presents some recent theoretical and computational results on Linear Algebra and Applications. The investigations developed in each one of its ten chapters have been written by one or more experts. They analyze subjects as quadratic forms, homogeneous matrix polynomials, linear control systems, Hermitian matrix-valued functions, triangular matrices, linear matrix equations, simultaneous triangularization over principal ideal domains and matrix differential equations, among others. Matrix Analysis Theory and Generalized Inverses are two extreme usefulness tools used to solve several of the proposed problems. In addition, settings such as the complex field or an arbitrary field, a ring or a quaternion algebra are the structures to work with. This interesting book is written in a very readable style and it is a very good contribution to the Linear Algebra Community and other interested readers." Reviewed by Nestor Thome, Professor, Department of Applied Mathematics of Polytechnical University of Valencia, Spain
"This is a worth-reading book about the recent developments in Linear Algebra and it includes contributions of fourteen authors from all over the world. The themes analyzed by the researchers in the ten chapters include quadratic optimization, matrix pencils, generalized inverses, matrix equations, maximal and minimal ranks and inertias, triangular matrices (tables) and their parafunctions, iterative methods, eigenvalues and eigenvectors, quasideterminants, regular rings and quaternions, among others. These developments have strong connections with other branches of mathematics like statistics, optimization, discrete mathematics and differential equations and they are related to important topics like fractals, graphs, power series, Markovian transitions and ODEs stability. Outside mathematics, potential applications to financial problems, electrical networks, filter design, chemical kinetics mechanisms and control theory, remark the importance of the topics considered. Finally, the inclusion of several open problems, numerical examples that clarify the theory and even a touch of humor in one of the footnotes, complete this interesting, enjoyable and easy readable book." - Review provided by Victor Martinez-Luaces, Profesor, Universidad de la República, Uruguay |
High Order Boundary Value Problems: Existence, Localization and Multiplicity Results
Authors:
João Fialho College of the Bahamas, Nassau, Bahamas Feliz Minhós Universidade de Évora, Évora, Portugal |
This very interesting book is devoted to the study of higher order boundary value problems. The main tool utilized throughout the volume is the method of upper and lower solutions. Of particular interest is the fact that in many cases the authors give an explicit construction of the upper and lower solution. The authors illustrate how this location tool can be utilized to gain qualitative information regarding the solutions: existence, multiplicity, monotonicity. Another nice feature of the book is that the methodology is applied also to real world phenomena: the London Millenium bridge and the periodic oscillations of the axis of a satellite. Overall the book is fairly easy to read and would be helpful for graduate students and young researchers willing to learn more on this method. - Reviewed by Gennaro Infante, Ph.D., Associate Professor, Department of Mathematics and Computer Science, University of Calabria, Italy
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Parallel Programming: Practical Aspects, Models and Current Limitations
Editor: Mikhail S. Tarkov
Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences, Russia |
This book has been reviewed by Olga L. Bandman, Chief Researcher, Professor, Institute of Computational Mathematics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia. To read the review,
click here. |
