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.

Kunquan Lan received his Ph. D in University of Glasgow, UK. He is a professor in the Department of Mathematics at Toronto Metropolitan University. His major research interests include Fractional Differential, Ordinary Differential Equations, Partial Differential Inequalities, Nonlinear Analysis, Mathematical Biology and Fluid dynamics. He has published more than 90 papers in good journals such as Plos One, Journal of Theoretical Biology, Journal of Differential Equations, Transactions of the American Mathematical Society, Proceedings of the American Mathematical Society, Journal of the London Mathematical Society, Bulletin of the London Mathematical Society, Proceedings A of the Royal Society of Edinburgh, Canadian Mathematical Bulletin, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Mathematical Methods in the Applied Sciences. Dr. Kunquan Lan serves as an associate editor of the Mathematical Methods in the Applied Sciences and editors for several journals.