  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.
