LEADER 04551nam 22006975 450 001 9910300245503321 005 20251223184954.0 010 $a3-319-25562-2 024 7 $a10.1007/978-3-319-25562-0 035 $a(CKB)3710000000602297 035 $a(SSID)ssj0001657918 035 $a(PQKBManifestationID)16441042 035 $a(PQKBTitleCode)TC0001657918 035 $a(PQKBWorkID)14989862 035 $a(PQKB)11721533 035 $a(DE-He213)978-3-319-25562-0 035 $a(MiAaPQ)EBC6313013 035 $a(MiAaPQ)EBC5595104 035 $a(Au-PeEL)EBL5595104 035 $a(OCoLC)1076231994 035 $a(PPN)192218794 035 $a(EXLCZ)993710000000602297 100 $a20160208d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aDiscrete Fractional Calculus /$fby Christopher Goodrich, Allan C. Peterson 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XIII, 556 p.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-319-25560-6 320 $aIncludes bibliographical references and index. 327 $aPreface -- 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. 330 $aThis 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. 606 $aDifferential equations 606 $aDifference equations 606 $aFunctional equations 606 $aFunctions of real variables 606 $aDifferential Equations 606 $aDifference and Functional Equations 606 $aReal Functions 615 0$aDifferential equations. 615 0$aDifference equations. 615 0$aFunctional equations. 615 0$aFunctions of real variables. 615 14$aDifferential Equations. 615 24$aDifference and Functional Equations. 615 24$aReal Functions. 676 $a515.625 700 $aGoodrich$b Christopher$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755686 702 $aPeterson$b Allan C$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300245503321 996 $aDiscrete Fractional Calculus$92509322 997 $aUNINA