The Analysis of Fractional Differential Equations

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.

From the reviews:

"This book treats a fast growing field of fractional differential equations, i.e., differential equations with derivatives of non-integer order. ... The book consists of two parts, eight chapters, an appendix, references and an index. ... The book is well written and easy to read. It could be used for, a course in the application of fractional calculus for students of applied mathematics and engineering." (Teodor M. Atanackovic, Mathematical Reviews, Issue 2011 j)

"This monograph is intended for use by graduate students, mathematicians and applied scientists who have an interest in fractional differential equations. The Caputo derivative is the main focus of the book, because of its relevance to applications. ... The monograph may be regarded as a fairly self-contained reference work and a comprehensive overview of the current state of the art. It contains many results and insights brought together for the first time, including some new material that has not,to my knowledge, appeared elsewhere." (Neville Ford, Zentralblatt MATH, Vol. 1215, 2011)