Discrete Fractional Calculus
Download Discrete Fractional Calculus full books in PDF, epub, and Kindle. Read online free Discrete Fractional Calculus ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author | : Christopher Goodrich |
Publisher | : Springer |
Total Pages | : 565 |
Release | : 2016-02-09 |
Genre | : Mathematics |
ISBN | : 3319255622 |
Download Discrete Fractional Calculus Book in PDF, Epub and Kindle
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.
Author | : Rui A. C. Ferreira |
Publisher | : Springer Nature |
Total Pages | : 95 |
Release | : 2022-03-14 |
Genre | : Mathematics |
ISBN | : 3030927245 |
Download Discrete Fractional Calculus and Fractional Difference Equations Book in PDF, Epub and Kindle
This brief aims to merge the theories of fractional calculus and discrete calculus in a concise but comprehensive manner. It is designed for graduate students, but will be useful for any researcher interested in the theory of discrete fractional calculus and fractional difference equations.
Author | : Piotr Ostalczyk |
Publisher | : World Scientific |
Total Pages | : 396 |
Release | : 2015-11-26 |
Genre | : Mathematics |
ISBN | : 9814725676 |
Download Discrete Fractional Calculus Book in PDF, Epub and Kindle
The main subject of the monograph is the fractional calculus in the discrete version. The volume is divided into three main parts. Part one contains a theoretical introduction to the classical and fractional-order discrete calculus where the fundamental role is played by the backward difference and sum. In the second part, selected applications of the discrete fractional calculus in the discrete system control theory are presented. In the discrete system identification, analysis and synthesis, one can consider integer or fractional models based on the fractional-order difference equations. The third part of the book is devoted to digital image processing.
Author | : Leo J. Grady |
Publisher | : Springer Science & Business Media |
Total Pages | : 371 |
Release | : 2010-07-23 |
Genre | : Computers |
ISBN | : 1849962901 |
Download Discrete Calculus Book in PDF, Epub and Kindle
This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Many example applications from several fields of computational science are provided.
Author | : Kenneth S. Miller |
Publisher | : Wiley-Interscience |
Total Pages | : 384 |
Release | : 1993-06-02 |
Genre | : Mathematics |
ISBN | : 9780471588849 |
Download An Introduction to the Fractional Calculus and Fractional Differential Equations Book in PDF, Epub and Kindle
Commences with the historical development of fractional calculus, its mathematical theory—particularly the Riemann-Liouville version. Numerous examples and theoretical applications of the theory are presented. Features topics associated with fractional differential equations. Discusses Weyl fractional calculus and some of its uses. Includes selected physical problems which lead to fractional differential or integral equations.
Author | : Dumitru Baleanu |
Publisher | : Springer Science & Business Media |
Total Pages | : 518 |
Release | : 2010-03-14 |
Genre | : Technology & Engineering |
ISBN | : 9048132932 |
Download New Trends in Nanotechnology and Fractional Calculus Applications Book in PDF, Epub and Kindle
In recent years fractional calculus has played an important role in various fields such as mechanics, electricity, chemistry, biology, economics, modeling, identification, control theory and signal processing. The scope of this book is to present the state of the art in the study of fractional systems and the application of fractional differentiation. Furthermore, the manufacture of nanowires is important for the design of nanosensors and the development of high-yield thin films is vital in procuring clean solar energy. This wide range of applications is of interest to engineers, physicists and mathematicians.
Author | : Igor Podlubny |
Publisher | : Elsevier |
Total Pages | : 366 |
Release | : 1998-10-27 |
Genre | : Mathematics |
ISBN | : 0080531989 |
Download Fractional Differential Equations Book in PDF, Epub and Kindle
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 | : Vasily E. Tarasov |
Publisher | : Springer Science & Business Media |
Total Pages | : 504 |
Release | : 2011-01-04 |
Genre | : Science |
ISBN | : 3642140033 |
Download Fractional Dynamics Book in PDF, Epub and Kindle
"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute.
Author | : Adel Ouannas |
Publisher | : World Scientific |
Total Pages | : 218 |
Release | : 2023-02-13 |
Genre | : Science |
ISBN | : 9811271224 |
Download Fractional Discrete Chaos: Theories, Methods And Applications Book in PDF, Epub and Kindle
In the nineteenth-century, fractional calculus had its origin in extending differentiation and integration operators from the integer-order case to the fractional-order case. Discrete fractional calculus has recently become an important research topic, useful in various science and engineering applications. The first definition of the fractional-order discrete-time/difference operator was introduced in 1974 by Diaz and Osler, where such operator was derived by discretizing the fractional-order continuous-time operator. Successfully, several types of fractional-order difference operators have then been proposed and introduced through further generalizing numerous classical operators, motivating several researchers to publish extensively on a new class of systems, viz the nonlinear fractional-order discrete-time systems (or simply, the fractional-order maps), and their chaotic behaviors. This discovery of chaos in such maps, has led to novel control methods for effectively stabilizing their chaotic dynamics.The aims of this book are as follows:
Author | : Yong Zhou |
Publisher | : World Scientific |
Total Pages | : 380 |
Release | : 2016-10-20 |
Genre | : Mathematics |
ISBN | : 9813148187 |
Download Basic Theory Of Fractional Differential Equations (Second Edition) Book in PDF, Epub and Kindle
This invaluable monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary and partial differential equations. It provides the readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, the technique of Picard operators, critical point theory and semigroup theory. Based on the research work carried out by the authors and other experts during the past seven years, the contents are very recent and comprehensive.In this edition, two new topics have been added, that is, fractional impulsive differential equations, and fractional partial differential equations including fractional Navier-Stokes equations and fractional diffusion equations.