Discrete Fractional Calculus - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Discrete Fractional Calculus write by Christopher Goodrich. This book was released on 2016-02-09. Discrete Fractional Calculus available 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.
Discrete Fractional Calculus and Fractional Difference Equations
Discrete Fractional Calculus and Fractional Difference Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Discrete Fractional Calculus and Fractional Difference Equations write by Rui A. C. Ferreira. This book was released on 2022-03-14. Discrete Fractional Calculus and Fractional Difference Equations available 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.
Discrete Fractional Calculus
Discrete Fractional Calculus - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Discrete Fractional Calculus write by Piotr Ostalczyk. This book was released on 2015-11-26. Discrete Fractional Calculus available 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.
Fractional Discrete Chaos: Theories, Methods And Applications
Fractional Discrete Chaos: Theories, Methods And Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fractional Discrete Chaos: Theories, Methods And Applications write by Adel Ouannas. This book was released on 2023-02-13. Fractional Discrete Chaos: Theories, Methods And Applications available 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:
Fractional Differential Equations
Fractional Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fractional Differential Equations write by Igor Podlubny. This book was released on 1998-10-27. Fractional Differential Equations available 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
