The problem of big data analytics is gaining increasing research interest because of the rapid growth in the volume of data to be analyzed in various areas of science and technology. In this paper, we investigate the characteristics of the cloud computing requests received by the cloud infrastructure operators. The cluster usage dataset released by Google is thoroughly studied. To address the self-similarity and non-stationarity characteristics of the workload profile in a cloud computing system, fractal modeling techniques similar to some cyber-physical system (CPS) applications are exploited. A trace-based prediction of the job inter-arrival time and aggregated resource request sent to server cluster in the near future is effectively performed by solving fractional-order differential equations. The distributions of important parameters including job/task duration time and resource request per task in terms of CPU, memory, and storage are extracted from the cluster dataset are fitted using the alpha-stable distribution.