In this thesis we established a common fixed point theorem for two hybrid pairs of single valued and multivalued mappings via subsequential continuity and d-compatibility, and we also prove the existence of a multivalued fixed point, by combining some new types of contractions , like the Geraghty type contractions with q-contraction and the notions of ?,h-admissible, certain consequences are given in metric spaces endowed with partial order or with graph.
Finally, we apply the results obtained to study the problem of the existence of the solution of fractional differential inclusions, and of a system of integral inclusions of the Volterra type