In this paper we analyze the asymptotic behavior of several fractional eigenvalue problems by means of Gamma-convergence methods. This method allows us to treat different eigenvalue problems under a unified framework. We are able to recover some known results for the behavior of the eigenvalues of the $ p- $fractional laplacian when the fractional parameter $ s $ goes to 1, and to extend some known results for the behavior of the same eigenvalue problem when $ p $ goes to $ \infty $. Finally we analyze other eigenvalue problems not previously covered in the literature.
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