Quasicrystals represent a unique class of long-range ordered structures characterized by orientational order but devoid of translational periodicity. In 1984, Israeli physicist D. Shechtman pioneered the discovery of this structure in tangible materials, sparking widespread interest within the condensed matter physics community. More recently, the revelation of superconductivity in Al-Zn-Mg and Ta_1.6Te quasicrystals has reignited research fervor, suggesting a pairing mechanism driven by electron-phonon coupling. Prior investigations primarily relied on mean-field methods to analyze simplified models, overlooking the retardation effects in interactions and thus failing to comprehensively capture the observed phenomena. Consequently, delving deeper into the superconductivity of quasicrystals necessitates the employment of more sophisticated methodologies to unravel its pairing mechanism.