The authors propose a wavelet-based decomposition of creep fluctuation signals recorded from living muscle precursor cells that revisit the traditional computation of their power spectrum from FFT-based decomposition. This decomposition offers a higher sensitivity for detecting the occurrence of fractional fluctuations and for quantitatively estimating the power-law exponent ² of this spectrum as a signature of the scale-invariant rheology of living cells. This new method has also the unprecedented advantage of providing a test of the validity of the commonly assumed 'monofractal' self-similar (as compared to 'multifractal' intermittent) nature of these fluctuations and hence accrediting the use of a single rheological exponent ± = ²/2. We report and discuss results obtained when applying this method to creep experiments performed with an AFM nanoindenter placed in contact with single myoblasts and myotubes, adherent on collagen coated coverslips, and in different culture conditions.