Prospecting black hole thermodynamics with fractional quantum mechanics

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