Author: Changpin Li (Mathematics professor) Publisher: ISBN: 9781611975871 Category : Fractional calculus Languages : en Pages : 312
Book Description
"This book provides a comprehensive review of fractional calculus, covering both theory and numerical methods, and presents recent results on the subject"--
Author: Changpin Li Publisher: SIAM ISBN: 1611975883 Category : Mathematics Languages : en Pages : 327
Book Description
Due to its ubiquity across a variety of fields in science and engineering, fractional calculus has gained momentum in industry and academia. While a number of books and papers introduce either fractional calculus or numerical approximations, no current literature provides a comprehensive collection of both topics. This monograph introduces fundamental information on fractional calculus, provides a detailed treatment of existing numerical approximations, and presents an inclusive review of fractional calculus in terms of theory and numerical methods and systematically examines almost all existing numerical approximations for fractional integrals and derivatives. The authors consider the relationship between the fractional Laplacian and the Riesz derivative, a key component absent from other related texts, and highlight recent developments, including their own research and results. The core audience spans several fractional communities, including those interested in fractional partial differential equations, the fractional Laplacian, and applied and computational mathematics. Advanced undergraduate and graduate students will find the material suitable as a primary or supplementary resource for their studies.
Author: Yuri Luchko Publisher: MDPI ISBN: 303650494X Category : Mathematics Languages : en Pages : 280
Book Description
This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. In particular, the “new fractional derivatives and integrals” and the models with these fractional order operators are critically addressed. The Special Issue contains both the surveys and the research contributions. A part of the articles deals with foundations of FC that are considered from the viewpoints of the pure and applied mathematics, and the system theory. Another part of the Special issue addresses the applications of the FC operators and the fractional differential equations. Several articles devoted to the numerical treatment of the FC operators and the fractional differential equations complete the Special Issue.
Author: Hossein Moosaei Publisher: Springer Nature ISBN: 3031503201 Category : Computers Languages : en Pages : 261
Book Description
This book constitutes the proceedings of the 6th International Conference on Dynamics of Information Systems, DIS 2023, which took place in Prague, Czech Republic, in September 2023. The 18 full papers included in the book were carefully reviewed and selected from 43 submissions. They deal with topics ranging from theoretical, algorithmic, and practical perspectives in information systems, to offering readers valuable information, theories and techniques.
Author: Ming Li Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110726157 Category : Mathematics Languages : en Pages : 334
Book Description
Vibration is important subject in many fields, ranging from mechanical engineering to electronic one. This book aims at giving a combination of conventional linear vibrations with recent fractional ones from a view of engineering. It consists of two parts. One is for conventional linear vibrations in Chapters 1 - 6 based on the authors lectures on the course of ship hull vibrations for undergraduates and postgraduates in Ocean College, Zhejiang University, China. The other, Chapters 7 - 15, contains his research in fractional vibrations. the book is suitable for researchers and graduate students in science and engieering. Preferred preliminaries are calculus, university physics, theoretic mechanics, and material mechanics for readers.
Author: Zhi-Zhong Sun Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110616068 Category : Mathematics Languages : en Pages : 396
Book Description
Starting with an introduction to fractional derivatives and numerical approximations, this book presents finite difference methods for fractional differential equations, including time-fractional sub-diffusion equations, time-fractional wave equations, and space-fractional differential equations, among others. Approximation methods for fractional derivatives are developed and approximate accuracies are analyzed in detail.
Author: Igor Podlubny Publisher: Elsevier ISBN: 0080531989 Category : Mathematics Languages : en Pages : 366
Book Description
This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'.This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models.In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research.A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. - A unique survey of many applications of fractional calculus - Presents basic theory - Includes a unified presentation of selected classical results, which are important for applications - Provides many examples - Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory - The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches - Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives
Author: Ming Li Publisher: CRC Press ISBN: 1003802540 Category : Technology & Engineering Languages : en Pages : 559
Book Description
The book examines vibration phenomena with an emphasis on fractional vibrations using the functional form of linear vibrations with frequency-dependent mass, damping, or stiffness, covering the theoretical analysis potentially applicable to structures and, in particular, ship hulls. Covering the six classes of fractional vibrators and seven classes of fractionally damped Euler-Bernoulli beams that play a major role in hull vibrations, this book presents analytical formulas of all results with concise expressions and elementary functions that set it apart from other recondite studies. The results show that equivalent mass or damping can be negative and depends on fractional orders. Other key highlights of the book include a concise mathematical explanation of the Rayleigh damping assumption, a novel description of the nonlinearity of fractional vibrations, and a new concept of fractional motion, offering exciting additions to the field of fractional vibrations. This title will be a must-read for students, mathematicians, physicists, and engineers interested in vibration phenomena and novel vibration performances, especially fractional vibrations.
Author: J. Sabatier Publisher: Springer Science & Business Media ISBN: 1402060424 Category : Technology & Engineering Languages : en Pages : 550
Book Description
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. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.
Author: Mouffak Benchohra Publisher: Springer Nature ISBN: 303134877X Category : Mathematics Languages : en Pages : 197
Book Description
This book covers problems involving a variety of fractional differential equations, as well as some involving the generalized Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations based on the most recent research in the area. The book discusses the classic and novel fixed point theorems related to the measure of noncompactness in Banach spaces and explains how to utilize them as tools. The authors build each chapter upon the previous one, helping readers to develop their understanding of the topic. The book includes illustrated results, analysis, and suggestions for further study.
Author: Changpin Li (Mathematics professor)
Author: Changpin Li
Author: Yuri Luchko
Author: Hossein Moosaei
Author: Ming Li
Author: Zhi-Zhong Sun
Author: Igor Podlubny
Author: Ming Li
Author: J. Sabatier
Author: Mouffak Benchohra