Fractional differential equations (FDEs), owing to their modeling potential in different branches of science and engineering, are attracting the attention of researchers. The concept of a fractional derivative is an extension of the classical derivative to a non-integer order derivative. Various types of fractional derivatives have been introduced, each being a generalization of an earlier version or having a certain advantage in a particular application. The present book consists of seven chapters selected to represent some of the current research trends in the area of fractional differential equations. The first two chapters present overviews of the stability theory of fractional differential equations and fractional-order difference equations, respectively. The next two chapters review existence results for two-point boundary value problems of nabla fractional difference equations and impulsive FDEs with variable moments of impulse, respectively. Chapter 5 introduces finite difference schemes for fractional diffusion equations. The tempered -Hilfer fractional derivative is used in Chapter 6 to study fuzzy random functional integro-differential equations. Chapter 7 deals with applications in FDEs of quantum-symmetric differential operators formulated via Raina functions.