An Example of the Generalized Fractional Laplacian on Rⁿ (Contemporary Mathematics, 2020)
Using the normalization of the fractional Laplacian (-△)su(x) over the space Ck(Rn ) for all s > 0 and s ≠ 1, 2, ···, we evaluate (-△)se-||x||2 based on the multidimensional surface integrals over the unit sphere and special functions.
Keywords: fractional Laplacian, normalization; distribution, surface integral, gamma function