Download Theory And Numerical Approximations Of Fractional Integrals And Derivatives full books in PDF, epub, and Kindle. Read online free Theory And Numerical Approximations Of Fractional Integrals And Derivatives ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : Changpin Li (Mathematics professor) |
| Publisher | : |
| Total Pages | : 312 |
| Release | : 2019 |
| Genre | : Fractional calculus |
| ISBN | : 9781611975871 |
"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 |
| Total Pages | : 327 |
| Release | : 2019-10-31 |
| Genre | : Mathematics |
| ISBN | : 1611975883 |
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 |
| Total Pages | : 280 |
| Release | : 2021-03-16 |
| Genre | : Mathematics |
| ISBN | : 303650494X |
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 | : Igor Podlubny |
| Publisher | : Elsevier |
| Total Pages | : 366 |
| Release | : 1998-10-27 |
| Genre | : Mathematics |
| ISBN | : 0080531989 |
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 | : Kai Diethelm |
| Publisher | : Springer |
| Total Pages | : 251 |
| Release | : 2010-08-18 |
| Genre | : Mathematics |
| ISBN | : 3642145744 |
Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.
| Author | : Changpin Li |
| Publisher | : CRC Press |
| Total Pages | : 300 |
| Release | : 2015-05-19 |
| Genre | : Mathematics |
| ISBN | : 148225381X |
Numerical Methods for Fractional Calculus presents numerical methods for fractional integrals and fractional derivatives, finite difference methods for fractional ordinary differential equations (FODEs) and fractional partial differential equations (FPDEs), and finite element methods for FPDEs.The book introduces the basic definitions and propertie
| Author | : J. Sabatier |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 550 |
| Release | : 2007-07-28 |
| Genre | : Technology & Engineering |
| ISBN | : 1402060424 |
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 | : Hossein Moosaei |
| Publisher | : Springer Nature |
| Total Pages | : 261 |
| Release | : 2024-01-28 |
| Genre | : Computers |
| ISBN | : 3031503201 |
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 |
| Total Pages | : 334 |
| Release | : 2021-03-08 |
| Genre | : Mathematics |
| ISBN | : 3110726157 |
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 | : Ricardo Almeida |
| Publisher | : Springer |
| Total Pages | : 135 |
| Release | : 2018-06-29 |
| Genre | : Technology & Engineering |
| ISBN | : 3319940066 |
The Variable-Order Fractional Calculus of Variations is devoted to the study of fractional operators with variable order and, in particular, variational problems involving variable-order operators. This brief presents a new numerical tool for the solution of differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one, an approximation formula is obtained in terms of standard (integer-order) derivatives only. Estimations for the error of the approximations are also provided. The contributors consider variational problems that may be subject to one or more constraints, where the functional depends on a combined Caputo derivative of variable fractional order. In particular, they establish necessary optimality conditions of Euler–Lagrange type. As the terminal point in the cost integral is free, as is the terminal state, transversality conditions are also obtained. The Variable-Order Fractional Calculus of Variations is a valuable source of information for researchers in mathematics, physics, engineering, control and optimization; it provides both analytical and numerical methods to deal with variational problems. It is also of interest to academics and postgraduates in these fields, as it solves multiple variational problems subject to one or more constraints in a single brief.
