This brief leads the synthesis of fractional‐order memristor (FOM) emulator circuits. To do so, a novel fractional‐order integrator (FOI) topology based on current‐feedback operational amplifier and integer‐order capacitors is proposed. Then, the FOI is substituting the integer‐order integrator inside flux‐ or charge‐controlled memristor emulator circuits previously reported in the literature and in both versions: floating and grounded. This demonstrates that FOM emulator circuits can also be configured at incremental or decremental mode and the main fingerprints of an integer‐order memristor are also holding up for FOMs. Theoretical results are validated through HSPICE simulations and the synthesized FOM emulator circuits can easily be reproducible. Moreover, the FOM emulator circuits can be used for improving future applications such as cellular neural networks, modulators, sensors, chaotic systems, relaxation oscillators, nonvolatile memory devices, and programmable analog circuits.