  We compute the quasinormal spectra for scalar, Dirac and electromagnetic
perturbations of the Schwarzschild-de Sitter geometry in the framework of
scale-dependent gravity, which is one of the current approaches to quantum
gravity. Adopting the widely used WKB semi-classical approximation, we
investigate the impact on the spectrum of the angular degree, the overtone
number as well as the scale-dependent parameter for fixed black hole mass and
cosmological constant. We summarize our numerical results in tables, and for
better visualization, we show them graphically as well. All modes are found to
be stable. Our findings show that both the real part and the absolute value of
the imaginary part of the frequencies increase with the parameter $\epsilon$
that measures the deviation from the classical geometry. Therefore, in the
framework of scale-dependent gravity the modes oscillate and decay faster in
comparison with their classical counterparts.
