This study derives the mass spectrum and entropy of the Brown–Kuchaˇr dust in anti-de Sitter (AdS) spacetime using the fractional Wheeler–DeWitt (WDW) equation. The generalized fractional WDW equation is formulated using a fractional quantization map, demonstrating a correlation between the fractal mass dimension of the Brown–Kuchaˇr dust and Lévy’s fractional parameter α of the Riesz fractional quantum operator. These findings may provide new insights into the ramifications of the fractal behavior of cosmic structures in quantum cosmology and quantum gravity.
