In this paper, we study the existence and multiplicity results for the following critical fractional Schrodinger equation with magnetic field epsilon(2)s(-delta)(s)(A/epsilon)q + V(x)q-lambda f(q)q- K(x)q(2 lowast;)(s) (-2)q = 0, in R-N, where epsilon > 0, lambda > 0, s is an element of (0, 1), N >= 3, 2(s)( lowast;) = 2N/N-2s , V : R-N -> R and A : R-N -> R-N are the electric and magnetic potentials respectively. The methods used here are based on the Nehari manifold method, Ekeland's variational principle and the Ljusternick-Schnirelmann category theory.
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