We first define some preliminaries, such as the gamma function, beta function, time convolution. We include some useful properties, some with proof. Then, we introduce the Riemann-Liouville (RL) fractional integral, and use it to define the RL fractional derivative. We show that the RL derivative has some unsatisfactory properties, and thus define the Caputo fractional time derivative to rectify these short comings. We then introduce the Mittag-Leffler function as a solution operator for some simple fractional differential equations. Time permitting, we may also briefly discuss the use of the Caputo derivative in the doubly non-local Cahn Hilliard Equation.