  This paper investigates whether the framework of fractional quantum mechanics
can broaden our perspective of black hole thermodynamics. Concretely, we employ
a {\it space-fractional} derivative \cite{Rie} as our main tool. Moreover, we
restrict our analysis to the case of a Schwarzschild configuration. From a
subsequently modified Wheeler-DeWitt equation, we retrieve the corresponding
expressions for specific observables. Namely, the black hole mass spectrum,
$M$, its temperature $T$, and entropy, $S$. We find that these bear
consequential alterations conveyed through a fractional parameter, $\alpha$. In
particular, the standard results are recovered in the specific limit
$\alpha=2$. Furthermore, we elaborate how generalizations of the entropy-area
relation suggested by Tsallis and Cirto \cite{Tsallis} and Barrow \cite{Barrow}
acquire a complementary interpretation in terms of a fractional point of view.
A thorough discussion of our results is presented.
