1.

Record Nr.

UNISA996466513703316

Autore

Diethelm Kai

Titolo

The Analysis of Fractional Differential Equations [[electronic resource] ] : An Application-Oriented Exposition Using Differential Operators of Caputo Type / / by Kai Diethelm

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2010

ISBN

1-280-39183-9

9786613569752

3-642-14574-4

Edizione

[1st ed. 2010.]

Descrizione fisica

1 online resource (VIII, 247 p. 10 illus.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 2004

Disciplina

515/.83

Soggetti

Differential equations

Integral equations

Mathematical analysis

Analysis (Mathematics)

Ordinary Differential Equations

Integral Equations

Analysis

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references (p. 237-244) and index.

Nota di contenuto

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.

Sommario/riassunto

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.