The aim of this book is to present a series of problems not yet investigated in the field of fractional differential equations. There are presented also a series of examples in the field of symbolic computation, written in Maple and Mathematica. It is introduced a new definition of the fractional derivative, in terms of translation operator. We introduced a new method, based on decomposition method and Laplace transform is presented in our previous LAP book. We studied also the fractional differential equations with the aid small parameter method. We used also the power series method. In the Chapter 5 it was established some predictor - corrector methods for fractional differential equations, of type Adams - Moulton, Adams-Bashforth, and Adams - Bashforth - Moulton. We investigated also the fractional integral equations. It was generalized the Galerkin and Ritz methods to the case of fractional differential equations. This book is addressed to a large category of readers, working in the field of fundamental and applied mathematics, theoretical physics, and experimental methods in physics and engineering.