Speaker diarization, the task of ascertaining speaker homogeneity within a collection of audio recordings featuring multiple speakers, is crucial for answering queries such as "who spoke when". Diverse speaker recordings, encompassing meetings, reality shows, and news broadcasts, typically populate the speaker diarization database. Traditional methods primarily rely on clustering speaker embeddings, yet these approaches often fail to minimize diarization errors effectively and struggle to accurately account for speaker overlaps. Addressing these limitations, we propose a robust model leveraging the Fractional Ebola Optimization Search Algorithm (FEOSA) for speaker segmentation and diarization. This model represents an amalgamation of the Fractional Calculus (FC) concept and the Ebola Optimization Search Algorithm (EOSA), thereby enhancing the efficacy of the diarization process. The diarization task is executed employing an entropy weighted power k-means algorithm, with weights updated via the proposed FEOSA. The proposed FEOSA demonstrated superior testing accuracy, reaching a maximum of 0.913, and significantly reduced diarization errors to a minimum of 0.566. Further, False Discovery Rate (FDR), False Negative Rate (FNR) and False Positive Rate (FPR) were recorded at 0.257, 0.128, and 0.104 respectively, underscoring the effectiveness of the proposed model in enhancing speaker diarization.