Other authors / contributors:  Peterson, Allan C., author.

ISBN:  9783319255620 3319255622 3319255606 9783319255606 9783319255606

Digital file characteristics:  text file PDF

Notes:  Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed February 17, 2016).

Summary:  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 integerorder 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 12 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 12 may be covered quickly and readers may then skip to Chapters 67 which present some basic results in fractional boundary value problems (FBVPs). Chapters 67 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 twosemester course, Chapters 15 may be covered in depth, providing a very thorough introduction to both the discrete fractional calculus as well as the integerorder calculus.

Other form:  Printed edition: 9783319255606

Standard no.:  10.1007/9783319255620
