This paper investigates the existence and uniqueness of solutions concerning fractional differential boundary value problems that incorporate the fractional \(p-\) Laplacian operator. These problems are defined within a finite interval and satisfy homogeneous boundary conditions. The solutions are characterized by their membership in fractional Sobolev spaces connected with \(\psi -\) generalized fractional operators. To approach these problems systematically, the paper establishes a variational formulation of the given system. This formulation proves to be instrumental in applying the variational method to establish the existence of a solution. The uniqueness of the solution is proven under certain conditions.
