The analysis of fractional differential equations: an application-oriented exposition using differential operators of Caputo type

Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have foundapplications 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 comparativelylittle 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. Providesa detailed mathematical description of the class fractional differential operators that is most important in applications in physics, engineering, etc. Bridges the gap between aspects from pure mathematics and application-oriented questions Contains a solid mathematical foundation on which researchers from outside of mathematics can build their models Is written in a style suitable for use as textbook INDICE: 1 Introduction.- 2 Riemann-Liouville Differential and Integral Operators.- 3 Caputo's Approach.- 4 Mittag-Leffler Functions.- 5 Existence and Uniqueness Results for Riemann-Liouville Fractional Differential Equations.- 6 Single-Term Caputo Fractional Differential Equations: Basic Theory and Fundamental Results.- 7 Single-Term Caputo Fractional Differential Equations: AdvancedResults for Special Cases.- 8 Multi-Term Caputo Fractional Differential Equations.

• ISBN: 978-3-642-14573-5
• Editorial: Springer
• Encuadernacion: Rústica
• Páginas: 246
• Fecha Publicación: 01/09/2010
• Nº Volúmenes: 1
• Idioma: Inglés