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| 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 | : 326 |
| 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 | : Hemen Dutta |
| Publisher | : John Wiley & Sons |
| Total Pages | : 336 |
| Release | : 2020-09-01 |
| Genre | : Mathematics |
| ISBN | : 1119654165 |
A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.
| 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 | : 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 | : 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 | : |
| Publisher | : Elsevier |
| Total Pages | : 252 |
| Release | : 1974-09-05 |
| Genre | : Mathematics |
| ISBN | : 0080956203 |
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression. - Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
| 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 | : 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.
