Weak and Strong points of the use of different kind of Fractional Derivatives to modeling the dynamics of anomalous processes Juan J. Trujillo Universidad de La Laguna Departamento de Análisis Matemática [email protected] ABSTRACT: It is well knows that exist a set of different Fractional Operators that can be used to model the dynamics of a number of Complex Systems. It also is easy to check that many branches of the Applied Sciences have find application to the Fractional Models. Here we will present some of the more known Fractional Operators and remark some of its properties, with the objective to point out the importance of the basics properties of such operators in connection with the Applied Problem that one would like to Model. As special case, we will illustrate such fact with a simple example in connection with some sub and/or super-diffusion fractional models.