Existence of three solution for fractional Hamiltonian system (Selecciones Matemáticas, 2017)
In this paper we consider the fractional Hamiltonian system given by(0.1)                       −tDα T(0Dα t u(t)) = ∇F(t,u(t)), a.e t ∈ [0,T]                                 u(0) = u(T) = 0.where α ∈ (1/2,1), t ∈ [0,T], u ∈Rn, F : [0,T]×Rn →R is a given function and ∇F(t,u) is the gradient of F at u. The novelty of this paper is that, using a modiﬁed version of mountain pass theorem for functional bounded from below we prove the existence of at least three solutions for (0.2).
Keywords: Fractional calculus; fractional derivatives; fractional Hamiltonian system; boundary value problem