Discrete Fractional Calculus by Allan C. Peterson download MOBI, EPUB, FB2
9783319255606 English 3319255606 The Fractional calculus is studied for both its theoretical interest as well as its use in applications. Within the past 5 7 years, there has been a surge of interest in developing a discrete fractional calculus to parallel the continuous theory. This text provides the first comprehensive treatment of the discrete fractional calculus and is appropriate for a myriad of potential courses. Several exercises are provided at the end of each chapter. The authors aim to maximize the flexibility of the text and its potential use in independent study. To this, select answers have been provided and most chapters may be covered or omitted, depending upon the background of the student. For example, the text may be used as primary in an introductory course in differential equations with the inclusion of discrete functional calculus. Chapters 1 2 provide a basic introduction to the delta calculus including fractional calculus on the time scale of integers. For courses where students already have background in elementary real analysis, Chapters 1 2 may be covered quickly and then one can skip to chapters 6 8 which present some basic results in fractional boundary value problems (FBVPs). Chapters 6 8 in conjunction with some of the current literature listed in the Bibliography can provide an easy basis for a seminar in the current theory of FBVPs. For a two-semester course, Chapters 1 5 may be covered carefully, providing a very thorough introduction to both the discrete fractional calculus as well as the integer-order time scale calculus. Students who are interested in learning about discrete fractional calculus will find this text to be a useful starting point and experienced researchers will find the text useful as a reference for Discrete Fractional Calculus (DFC) as well as related topics of current interest.", 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.
9783319255606 English 3319255606 The Fractional calculus is studied for both its theoretical interest as well as its use in applications. Within the past 5 7 years, there has been a surge of interest in developing a discrete fractional calculus to parallel the continuous theory. This text provides the first comprehensive treatment of the discrete fractional calculus and is appropriate for a myriad of potential courses. Several exercises are provided at the end of each chapter. The authors aim to maximize the flexibility of the text and its potential use in independent study. To this, select answers have been provided and most chapters may be covered or omitted, depending upon the background of the student. For example, the text may be used as primary in an introductory course in differential equations with the inclusion of discrete functional calculus. Chapters 1 2 provide a basic introduction to the delta calculus including fractional calculus on the time scale of integers. For courses where students already have background in elementary real analysis, Chapters 1 2 may be covered quickly and then one can skip to chapters 6 8 which present some basic results in fractional boundary value problems (FBVPs). Chapters 6 8 in conjunction with some of the current literature listed in the Bibliography can provide an easy basis for a seminar in the current theory of FBVPs. For a two-semester course, Chapters 1 5 may be covered carefully, providing a very thorough introduction to both the discrete fractional calculus as well as the integer-order time scale calculus. Students who are interested in learning about discrete fractional calculus will find this text to be a useful starting point and experienced researchers will find the text useful as a reference for Discrete Fractional Calculus (DFC) as well as related topics of current interest.", 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.