The main purpose of this work is to study the fractional order linear and nonlinear differential equations. This book is to present the analytical solutions of fractional order differential equations. The book is divided into two main parts: (a) - The fractional order ordinary and (b) - The fractional order partial differential equations. The aim of presenting, in a systematic manner, results including the solutions of linear and nonlinear system of fractional order equations arising in chemical kinetics by homotopy and variational methods, fractional order Riccati differential equations by less computational homotopy approach, explicit solutions of linear and nonlinear system of fractional order differential equations, nonlinear fractional order Swift–Hohenberg (S-H) equation, the fractional order Burgers equations and the time-fractional reaction-diffusion equations. The non-perturbative and numerical methods have been implemented to obtain the solutions of considered problems. Results will be developed which are useful for the researchers and it is also useful which will interact to its practical applications with engineers and mathematician.