Discrete Fractional Calculus

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This text offers a comprehensive treatment of discrete fractional calculus, serving as a valuable reference for experienced researchers and a solid starting point for students. Each chapter includes exercises, with select answers provided at the end of the book, fostering independent study and flexibility for various courses. The authors present a novel approach by simultaneously addressing fractional- and integer-order difference calculus across different time scales, including forward and backward difference operators. Readers will gain a foundational understanding of classical discrete calculus while exploring recent developments in the field. Chapters can be tailored to the student's background; for instance, those with prior knowledge in elementary real analysis may quickly cover the introductory Chapters 1-2 and proceed to Chapters 6-7, which delve into fractional boundary value problems (FBVPs). These chapters, alongside current literature referenced in the Bibliography, can support a seminar on FBVP theory. For a two-semester course, an in-depth exploration of Chapters 1-5 offers a thorough introduction to both discrete fractional and integer-order calculus.