  We study the following fractional elliptic equations of the type,
\begin{equation*} (-\Delta)^{\frac12}_A u = \lambda u+f(|u|)u ,\;\textrm{in }
\;(-1, 1),\; u=0\;\textrm{in } \;\mathbb R\setminus (-1, 1), \end{equation*}
where $\lambda$ is a positive real parameter and $(-\Delta)^{\frac12}_A$ is the
fractional magnetic operator with $A:\mathbb R\to \mathbb R$ being a smooth
magnetic field. Using a classical critical point theorems, we prove the
existence of multiple solutions in the non-resonant case when the nonlinear
term $f(t)$ has a critical exponential growth in the sense of Trudinger-Moser
inequality.
