In recent years, due to its non-volatile memory, non-locality, and weak singularity features, fractional calculations have begun to take place frequently in artificial neural network implementations and learning algorithms. Therefore, there is a need for circuit element implementations providing fractional function behaviors for the physical realization of these neural networks. In this study, a previously defined integer order memristor element equation is changed and a fractional order memristor is given in a similar structure. By using the obtained mathematical equation, frequency-dependent pinched hysteresis loops are obtained. A memristance simulator circuit that provides the proposed mathematical relationship is proposed. Spice simulations of the circuit are run and it is seen that they are in good agreement with the theory. Also, the non-volatility feature has been demonstrated with Spice simulations. The proposed circuit can be realized by using the integrated circuit elements available on the market. With a small connection change, the proposed structure can be used to produce both positive and negative memristance values.