Summary: We demonstrate that fractional Laplacian (FL) is the principal characteristic operator of harmonic systems with self-similar interparticle interactions. We show that the FL represents the ‘fractional continuum limit’ of a discrete ‘self-similar Laplacian’ which is obtained by Hamilton’s variational principle from a discrete spring model. We deduce from generalized self-similar elastic potentials regular representations for the FL which involve convolutions of symmetric finite difference operators of even orders extending the standard representation of the FL. Further we deduce a regularized representation for the FL \(-(-\Delta)^{\alpha/2}\) holding for \(\alpha \in \mathbb{R} \geqslant 0\). We give an explicit proof that the regularized representation of the FL gives for integer powers \(\alpha/2 \in \mathbb{N}_{0}\) a distributional representation of the integer powers of standard Laplacian operator \(\Delta\) including the trivial unity operator for \(\alpha \to 0\). We demonstrate that self-similar harmonic systems are governed in a distributional sense by this regularized representation of the FL which therefore can be conceived as characteristic footprint of self-similarity.