The Analysis of Fractional Differential Equations An Application-Oriented Exposition Using Differential Operators of Caputo Type /

• Main Author: Diethelm, Kai (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Lecture Notes in Mathematics, 2004
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Integral equations.; Differential equations.; Ordinary Differential Equations.; Integral Equations.; Analysis.

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 partic...

Table of Contents:

• 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.