Bifurcation results for a class of fractional Hamiltonian systems with Liouville–Weyl fractional derivatives

Abstract

In this paper, by using variational methods, we prove the existence for a class of fractional Hamiltonian systems with Liouville–Weyl fractional derivatives { t D ∞ α ( - ∞ D t α u ( t ) ) + b ( t ) u ( t ) - λ u ( t ) = μ f ( t , u ( t ) ) , t ∈ ℝ u ∈ H α ( ℝ ) where and are the right and left inverse operators of the corresponding Liouville–Weyl fractional integrals of order α respectively, , are real parameters and is a function that satisfies some suitable conditions.