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We study the existence of nontrivial solutions for a nonlinear fractionalelliptic equation in presence of logarithmic and critical exponentialnonlinearities. This problem extends [5] to fractional $N/s$-Laplacianequations with logarithmic nonlinearity. We overcome the lack of compactnessdue to the critical exponential nonlinearity by using the fractionalTrudinger-Moser inequality. The existence result is established via criticalpoint theory.

Existence result for fractional problems with logarithmic and critical exponential nonlinearities