03587nam 2200649Ia 450 991048426120332120200520144314.09786613569752978128039183512803918399783642145742364214574410.1007/978-3-642-14574-2(CKB)2670000000036600(SSID)ssj0000449013(PQKBManifestationID)11300454(PQKBTitleCode)TC0000449013(PQKBWorkID)10392763(PQKB)11469625(DE-He213)978-3-642-14574-2(MiAaPQ)EBC3065679(PPN)149019998(EXLCZ)99267000000003660020100927d2010 uy 0engurnn|008mamaatxtccrThe analysis of fractional differential equations an application-oriented exposition using differential operators of Caputo type /Kai Diethelm1st ed. 2010.Berlin Springerc20101 online resource (VIII, 247 p. 10 illus.) Lecture notes in mathematics,1617-9692 ;2004Bibliographic Level Mode of Issuance: Monograph9781671668454 1671668456 9783642145735 3642145736 Includes bibliographical references (p. 237-244) and index.Fundamentals of Fractional Calculus -- Riemann-Liouville Differential and Integral Operators -- Caputo’s Approach -- Mittag-Leffler Functions -- Theory of Fractional Differential Equations -- Existence and Uniqueness Results for Riemann-Liouville Fractional Differential Equations -- Single-Term Caputo Fractional Differential Equations: Basic Theory and Fundamental Results -- Single-Term Caputo Fractional Differential Equations: Advanced Results for Special Cases -- Multi-Term Caputo Fractional Differential Equations.Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.Lecture notes in mathematics (Springer-Verlag) ;2004.Application-oriented exposition using differential operators of Caputo typeDifferential equationsFractional calculusDifferential equations.Fractional calculus.515/.83Diethelm Kai478947MiAaPQMiAaPQMiAaPQBOOK9910484261203321The Analysis of Fractional Differential Equations2831263UNINA