With the increasing adoption of electric vehicles (EVs) on urban roads, traditional traffic management approaches that treat all vehicles equally are no longer sufficient to address the diverse impacts of EVs and conventional vehicles (CVs). This paper proposes a fair management approach addressing the distinct characteristics of EVs and CVs, focusing on optimizing traffic signal control to promote fair road usage and reduce delays. We introduce a fairness function that considers vehicle-specific attributes, including waiting times and vehicle credits, to allocate traffic signal resources in a way that supports both environmental goals and balanced access for all vehicle types. The effectiveness of this approach is demonstrated through two key analyses: delay heatmaps for multiple intersections before and after implementing the fair management strategy, and an evaluation of the impact of varying EV penetration rates on balanced and unbalanced traffic conditions. The results show that the proposed fairness function not only decreases delays but also improves overall traffic flow, particularly in scenarios with higher EV penetration. This study contributes to the development of sustainable urban traffic systems by promoting a fair transition towards greener and more efficient transportation systems.