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In this paper, we deal with the fractional-Laplacian problem with nonlocal Neumann boundary conditionshereare parameters andare two nonnegative weighted functions. The domainis smooth and bounded,are continuous bounded functions. Applying the Ekeland principle and the variational method, under appropriate assumptions, we show that the above problem has nontrivial weak solutions.

The fractional p (.,.)-Neumann boundary conditions for the nonlocal p (.,.)-Laplacian operator