Existence and symmetric result for Liouville-Weyl fractional nonlinear Schrodinger equation

We study the existence of positive solution for the one dimensional Schrodinger equation with mixed Liouville-Weyl fractional derivatives tD(infinity)(proportional to)((-infinity)D(t)(proportional to)u(t)) + B(t)u(t) = f(u(t)), t is an element of R u is an element of H-proportional to(R). Furthermore, we analyse radial symmetry property of these solutions. The proof is carried out by using variational methods jointly with comparison and rearrangement argument. (C) 2015 Published by Elsevier B.V.