Discrete Fractional Calculus

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.