Discrete fractional calculus / Christopher Goodrich, Allan C. Peterson

• Autore: Goodrich, Christopher
• Pubblicazione: [Cham], : Springer, 2015
• Titolo uniforme: Discrete fractional calculus
• Descrizione fisica: XIII, 556 p. : ill. ; 24 cm
• Soggetto topico: 26A33 - Fractional derivatives and integrals [MSC 2020]; 26E70 - Real analysis on time scales or measure chains [MSC 2020]; 34E10 - Perturbations, asymptotics of solutions to ordinary differential equation [MSC 2020]; 34Nxx - Dynamic equations on time scales or measure chains [MSC 2020]; 39A10 - Additive difference equations [MSC 2020]; 39A12 - Discrete version of topics in analysis [MSC 2020]; 39Axx - Difference equations [MSC 2020]
• Soggetto non controllato: Delta Laplace transform; Difference calculus; Discrete fractional calculus; Discrete nabla integral; Floquet Theory; Fractional boundary value problems; Fractional power rules; Green's Function; Integer-order time scale calculus; Laplace transforms; Mittag-Leffler function; Nabla exponential function; Nabla fractional calculus; Ordinary Differential Equations; Quantum calculus
• Altri autori: Peterson, Allan C.
• Nota di contenuto: 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.
• Titolo autorizzato: Discrete fractional calculus
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: VAN00113885
• Lo trovi qui: Univ. Vanvitelli
• Localizzazioni e accesso elettronico: http://dx.doi.org/10.1007/978-3-319-25562-0