  In this paper we establish, using variational methods combined with the
Moser-Trudinger inequality, existence and multiplicity of weak solutions for a
class of critical fractional elliptic equations with exponential growth without
a Ambrosetti-Rabinowitz-type condition. The interaction of the nonlinearities
with the spectrum of the fractional operator will used to study the existence
and multiplicity of solutions. The main technical result proves that a local
minimum in $C_{s}^0(\overline{\Omega})$ is also a local minimum in $W^{s,p}_0$
for nonlinearities with exponential growth.
