Soltani Nor El Houda2022-12-052022-12-052021-06-10https://dspace.univ-annaba.dz//handle/123456789/740The work presented in this thesis is devoted to studying the existence and multiplicity of non-trivial positive solutions of a singular fractional elliptic type system associated with the fractional p-Laplacian operator in a bounded domain R N . The results are obtained using some of the variational techniques, Nehari Manifold, Fibering method (F.M), and applying the Ekeland variational principle.en