The physical conception of the memristor by the Hewlett-Packard Labs has opened the possibility of combining this new fundamental circuit element with traditional devices in order to carried out novel applications. An important step for incorporating the memristor into the computer-aided design tools is to find an expression that represents the behavior of the device. In this paper, a novel modeling methodology for memristive systems using homotopy perturbation methods is introduced. This methodology is capable of generating a semi-symbolical expression that represents the memristive behavior of the device. The new memristor model is characterized in order to determinate the impact of the variables on the memristive behavior and establishes the range of compliance using the principal fingerprints of the memristor. Besides, the novel memristor model is depicted by two cases of study. Finally, the advantages of the memristor model are presented and discussed.