<p>This study uses the Krylov–Bogoliubov averaging method to investigate the dynamics of a piezoelectric energy harvesting system. The system has a fractional-order current–voltage relationship in the circuit and a fractional power-law mechanical restoring force. The analysis focuses on two central fractional parameters: the fractional deflection exponent and the fractional derivative order. The results show that the effect of the fractional derivative order strongly depends on the excitation amplitude. Under weak excitation, a smaller fractional derivative order reduces the resonant amplitude and slightly broadens the bandwidth. Under strong excitation, the hardening behavior becomes pronounced, the frequency-amplitude response curve shows multivalued branches, and the energy harvesting efficiency improves. Similarly, the effect of the fractional deflection exponent also varies with the excitation level. Under weak excitation, a smaller fractional deflection exponent lowers the equivalent linear stiffness. This reduces the resonance peak but causes the system to enter the nonlinear hardening regime earlier. Under strong excitation, a larger fractional deflection exponent leads to stronger hardening, a lower and narrower resonance peak, and the appearance of multiple amplitude solutions. Notably, the coupling of the two fractional effects produces new dynamic phenomena, such as increased output power, enhanced bandwidth, and multistability. In addition, the study analyses the influence of other parameters and performs a multi-objective optimization to maximize the peak output power and bandwidth. The trade-off between the two objectives is quantified, and a balanced parameter set is provided. Through numerical simulations, the combined effects of the fractional orders and noise intensity on system performance under random excitation are also thoroughly examined.</p>