  The use of fractional differential equations is a key tool in modeling
non-local phenomena. Often, an efficient scheme for solving a linear system
involving the discretization of a fractional operator is evaluating the matrix
function $x = \mathcal A^{-\alpha} c$, where $\mathcal A$ is a discretization
of the classical Laplacian, and $\alpha$ a fractional exponent between $0$ and
$1$. In this work, we derive an exponential sum approximation for $f(z)
=z^{-\alpha}$ that is accurate over $[1, \infty)$ and allows to efficiently
approximate the action of bounded and unbounded operators of this kind on
tensors stored in a variety of low-rank formats (CP, TT, Tucker). The results
are relevant from a theoretical perspective as well, as they predict the
low-rank approximability of the solutions of these linear systems in low-rank
tensor formats.
