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On the fractional Laplacian of variable order (2109.01060v1)
Published 2 Sep 2021 in math.AP, math-ph, and math.MP
Abstract: We present a novel definition of variable-order fractional Laplacian on Rn based on a natural generalization of the standard Riesz potential. Our definition holds for values of the fractional parameter spanning the entire open set (0, n/2). We then discuss some properties of the fractional Poisson's equation involving this operator and we compute the corresponding Green function, for which we provide some instructive examples for specific problems.
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