We study the existence of weak solution for a non-linear problem with fractional p-Laplacian operator for the case where the order of the fractional derivative is 1/pp < alfa < 1, 1 < q < p-1, with 2 < p <Infinito, then using the minimization method called Nehari Manifold and its important relationship with the Fibering Maps, whichis defined in the form t-->J(tu), where J is the functional associated to the non-linear problem to be studied, the main result is obtained.

We study the existence of weak solution for a non-linear problem with fractional p-Laplacian operator for the case where the order of the fractional derivative is 1/pp < alfa < 1, 1 < q < p-1, with 2 < p <Infinito, then using the minimization method called Nehari Manifold and its important relationship with the Fibering Maps, whichis defined in the form t-->J(tu), where J is the functional associated to the non-linear problem to be studied, the main result is obtained.