With the increase in the discovery of vulnerabilities, the expected exploits occurred in various software platform has shown an increased growth with respect to time. Only after being discovered, the potential vulnerabilities might be exploited. There exists a finite time lag in the exploitation process; from the moment the hackers get information about the discovery of a vulnerability and the time required in the final exploitation. By making use of the time lag approach, we have developed a framework for the vulnerability exploitation process that occurred in multiple stages. The time lag between the discovery and exploitation of a vulnerability has been bridged via the memory kernel function over a finite time interval. The applicability of the proposed model has been validated using various software exploit datasets.