Existence de Solutions pour un Probleme Non Lineaire d’une Equation Differentielle Fractionnaire Implicite

Abstract

The main objective of this paper is to study the existence of solutions for a nonlinear problem of an implicit fractional differential equation. The derivatives considered are in the sense of Caputo and of order between 0 and 1 in a Banach space with boundary conditions and in the second case with non-local ones. These results were obtained by applying the fixed point theory. Examples are included to illustrate the applicability of theoretical results.