Discrete Fractional Calculus

Allan C. Peterson is professor of mathematics at the University of Nebraska, Lincoln. Peterson, with Walter Kelley, is author of "The Theory of Differential Equations", (c) 2010, Universitext. Current research interests include dynamic equations on time scales, fractional calculus, difference equations, and differential equations.Christopher Goodrich is currently a mathematics instructor at the Creighton Preparatory School in Omaha, Nebraska.

• Preface.- 1. Basic Difference Calculus.- 2. Discrete Delta Fractional Calculus and Laplace Transforms.- 3. Nabla Fractional Calculus.- 4. Quantum Calculus.- 5. Calculus on Mixed Time Scales.- 6. Fractional Boundary Value Problems.- 7. Nonlocal BVPs and the Discrete Fractional Calculus.-Solutions to Selected Problems.- Bibliography.- Index.

“This textbook is the first dedicated solely to the study of this field. … this textbook is very well written and easy to follow. … Each chapter ends with numerous exercises. This book will be very useful to those studying fractional calculus in general and discrete fractional calculus. It will also be useful as a textbook for a course in discrete fractional calculus.” (Mohammad Sal Moslehian, zbMATH 1350.39001, 2017)“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)