This Letter demonstrates the nonlinear conversion of asymmetric perfect vortex (APV) beams with fractional orbital angular momentum (OAM). By controlling the amplitude and phase of the fundamental light field, we create APVs whose global OAM demonstrates a one-to-one correspondence of the charge numbers for fractional OAM values. The results show that the OAM of the second-harmonic generation fields follow the OAM conservation law. The nonlinear interactions of multiple OAM beams with the APVs are also investigated as they relate to the nonlinear frequency conversion and are shown to exhibit unique frequencies as a result of the Doppler frequency tagged OAM values.