In the last few years, the use of fractional derivatives (and integrals) to model physical phenomena, increased significantly. The reason for such success comes from the fact that these fractional operators seem to naturally generalize the differential equations governing important physical processes, improving their range of applicability.
In this work we will present the background theory that supports such operators, we will derive numerical methods for the solution of certain fractional differential equations and we will also present the theory connecting these fractional models to diffusion and elasticity.