Coincidence Degree and Fixed Point Theory Applied to the Study of Solutions of a Nonlinear Fractional Boundary Value Problem

This work is devoted to the study of a class of fractional boundary value problems using the (left) Caputo derivative and with the particularity of being resonant, i.e., the associated homogeneous problem admits a nontrivial solution. Conditions to ensure the existence and uniqueness of solutions are presented. Using Mawhin’s coincidence degree, it is shown that the problem under consideration admits solutions, and applying the Banach contraction principle, sufficient conditions are obtained for which the solution is unique.