The recent advancements in information technology and the web tend to increase the volume of data used in day-to-day life. The result is a big data era, which has become a key issue in research due to the complexity in the analysis of big data. This paper presents a technique called FPWhale-MRF for big data clustering using the MapReduce framework (MRF), by proposing two clustering algorithms. In FPWhale-MRF, the mapper function estimates the cluster centroids using the Fractional Tangential-Spherical Kernel clustering algorithm, which is developed by integrating the fractional theory into a Tangential-Spherical Kernel clustering approach. The reducer combines the mapper outputs to find the optimal centroids using the proposed Particle-Whale (P-Whale) algorithm, for the clustering. The P-Whale algorithm is proposed by combining Whale Optimization Algorithm with Particle Swarm Optimization, for effective clustering such that its performance is improved. Two datasets, namely localization and skin segmentation datasets, are used for the experimentation and the performance is evaluated regarding two performance evaluation metrics: clustering accuracy and DB-index. The maximum accuracy attained by the proposed FPWhale-MRF technique is 87.91% and 90% for the localization and skin segmentation datasets, respectively, thus proving its effectiveness in big data clustering.