Table of contents

  1. Front Matter
    Pages i-xiii
  2. Christopher Goodrich, Allan C. Peterson
    Pages 1-86
  3. Christopher Goodrich, Allan C. Peterson
    Pages 87-147
  4. Christopher Goodrich, Allan C. Peterson
    Pages 149-285
  5. Christopher Goodrich, Allan C. Peterson
    Pages 287-351
  6. Christopher Goodrich, Allan C. Peterson
    Pages 353-414
  7. Christopher Goodrich, Allan C. Peterson
    Pages 415-456
  8. Christopher Goodrich, Allan C. Peterson
    Pages 457-539
  9. Back Matter
    Pages 541-556

About this book

Introduction

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

Authors and affiliations

  • Christopher Goodrich
    • 1
  • Allan C. Peterson
    • 2
  1. 1.Creighton Preparatory SchoolKingstonUSA
  2. 2.LincolnUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-25562-0
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-25560-6
  • Online ISBN 978-3-319-25562-0
  • About this book