This paper investigates whether the framework of fractional quantum mechanics can broaden our perspective of black hole thermodynamics. Concretely, we employ a space-fractional derivative (Riesz in Acta Math 81:1, 1949) 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 (Eur Phys J C 73:2487, 2013) and Barrow (Phys Lett B 808:135643, 2020) acquire a complementary interpretation in terms of a fractional point of view. A thorough discussion of our results is presented.

本文研究分数量子力学的框架是否可以拓宽我们对黑洞热力学的看法。具体而言，我们采用空间分数导数（Riesz in Acta Math 81:1, 1949）作为我们的主要工具。此外，我们将分析限制在 Schwarzschild 配置的情况下。从随后修改的 Wheeler-DeWitt 方程中，我们检索特定可观察量的相应表达式。即，黑洞质谱M、其温度T和熵S。我们发现这些通过分数参数\(\alpha \)传达的相应改变。特别是在特定限度内恢复标准结果\(\alpha =2\)。此外，我们详细说明了 Tsallis 和 Cirto (Eur Phys JC 73:2487, 2013) 和 Barrow (Phys Lett B 808:135643, 2020) 建议的熵-面积关系的概括如何获得补充解释看法。对我们的结果进行了彻底的讨论。