Inspired by an abundance of existing flaws in the literature on fractional differential equations, this book serves an important purpose by providing a meticulous presentation with new insights. Placing the topics on a firm theoretical foundation, it is designed for researchers and students who already have a base of understanding to build on. It is a solid reference which may also be used as either a supplementary or a primary text in a course in fractional calculus.
The book provides precise and correct versions of the following topics: Riemann-Liouville (R-L) fractional integrals; R-L type fractional derivatives and Caputo fractional derivatives; equivalences of linear or nonlinear first order or higher order R-L type or Caputo FDEs; Abel type R-L integral equations; the identities of the R-L fractional integrals composed with the corresponding R-L type or Caputo fractional derivatives. The exposition is mostly self-contained. For the few classical theorems whose proofs are not provided, it is clearly noted where proofs may be found.
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