In this thesis, we have studied some essential properties of the topological degree for compact perturbations of the identity or respect to a Fredholm operator of index zero.
This theoretical part occupies the first part of the thesis, which begins with some preliminaries about functional analysis. Next, we presented preminaries about the topological degree of Brouwer and Leray-Schauder, Mawhin's coincidence degree and some fundamental properties and theories related to it.
The second part is entirely devoted to the applications of this tool to the resolution of boundary problems associated with nonlinear fractional differential equations at resonance case by using the Mawhin coincidence theory.