The paper presents an experimental study on higher-order and fractional discrete time crystals (DTCs) in Floquet-driven Rydberg atomic gases. The authors demonstrate a method to observe these exotic phases, which have been theoretically studied but not experimentally probed in quantum many-body systems. They discover multiple integer-order DTCs with values of \( n = 2, 3, 4 \), and up to \( n = 14 \), as well as fractional DTCs with values beyond integers. The system's response transitions between adjacent integer DTCs, revealing fractional DTCs during this process. The study expands the understanding of non-equilibrium dynamics and opens new avenues for exploring complex temporal symmetries. The experimental results align well with theoretical predictions, highlighting the rich dynamics that can emerge from driven and dissipative systems. The findings contribute to the theory of DTCs and provide insights into the symmetry breaking in driven quantum systems.The paper presents an experimental study on higher-order and fractional discrete time crystals (DTCs) in Floquet-driven Rydberg atomic gases. The authors demonstrate a method to observe these exotic phases, which have been theoretically studied but not experimentally probed in quantum many-body systems. They discover multiple integer-order DTCs with values of \( n = 2, 3, 4 \), and up to \( n = 14 \), as well as fractional DTCs with values beyond integers. The system's response transitions between adjacent integer DTCs, revealing fractional DTCs during this process. The study expands the understanding of non-equilibrium dynamics and opens new avenues for exploring complex temporal symmetries. The experimental results align well with theoretical predictions, highlighting the rich dynamics that can emerge from driven and dissipative systems. The findings contribute to the theory of DTCs and provide insights into the symmetry breaking in driven quantum systems.