ABSTRACT
In this chapter, we address the numerical approximation of the fractional diffusion equation with a reaction term. We specially present the stability and convergence of our numerical discretization, in the context of fractional calculus. The investigations and analysis concern the fractional differential equation described by the Caputo generalized fractional time derivative. We present the existence and uniqueness of the solution of the fractional diffusion equation. We use the classical Banach fixed theorem in our studies. Graphical representations of the solutions have been presented to illustrate the main results of the chapter.
