Authors:
May be used for courses at the upper undergraduate level and above; the field is promoted by specialists
Flexibility in its use, the text covers all aspects of discrete functional calculus
Contains good examples, suitable problems, and comprehensive coverage of the topic
Includes supplementary material: sn.pub/extras
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Table of contents (7 chapters)
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Front Matter
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Back Matter
About this book
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.Keywords
- Nabla fractional calculus
- discrete fractional calculus
- fractional boundary value problems
- integer-order time scale calculus
- quantam calculus
- discrete fractional calculus textbook adoption
- difference calculus
- Laplace transforms
- Delta Laplace transform
- fractional power rules
- nabla exponential function
- discrete nabla integral
- Mittag-Leffler function
- quantum calculus
- Floquet theory
- Green's function
- ordinary differential equations
Reviews
“This book offers a broad perspective on discrete fractional calculus … . The book, which includes problem sets, is written, so that it can be used as a textbook. The early chapters begin with the basics, and so the book can be used for a student’s first exposure to discrete calculus. The book also covers topics of current research interest with careful attention to techniques and calculations; hence the book is appropriate for advanced seminars in discrete fractional calculus.” (P. W. Eloe, Mathematical Reviews, July, 2016)
Authors and Affiliations
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Creighton Preparatory School, Kingston, USA
Christopher Goodrich
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Lincoln, USA
Allan C. Peterson
About the authors
Bibliographic Information
Book Title: Discrete Fractional Calculus
Authors: Christopher Goodrich, Allan C. Peterson
DOI: https://doi.org/10.1007/978-3-319-25562-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-25560-6Published: 17 February 2016
Softcover ISBN: 978-3-319-79809-7Published: 30 March 2018
eBook ISBN: 978-3-319-25562-0Published: 09 February 2016
Edition Number: 1
Number of Pages: XIII, 556
Topics: Differential Equations, Difference and Functional Equations, Real Functions