Modeling, simulation, and prediction of global energy indices remain veritable tools for econometric, engineering, analysis, and prediction of energy indices. Thus, this paper differentially modeled, simulated, and non-differentially predicated the global energy indices. The state-of-the-art of the research includes normalization of energy indices, generation of differential rate terms, and regression of rate terms against energy indices to generate coefficients and unexplained terms. On imposition of initial conditions, the solution to the system of linear differential equations was realized in a Matlab environment. There was a strong agreement between the simulated and the field data. The exact solutions are ideal for interpolative prediction of historic data. Furthermore, the simulated data were upgraded for extrapolative prediction of energy indices by introducing an innovative model, which is the synergy of deflated and inflated prediction factors. The innovative model yielded a trendy prediction data for energy consumption, gross domestic product, carbon dioxide emission and human development index. However, the oil price was untrendy, which could be attributed to odd circumstances. Moreover, the sensitivity of the differential rate terms was instrumental in discovering the overwhelming effect of independent indices on the dependent index. Clearly, this paper has accomplished interpolative and extrapolative prediction of energy indices and equally recommends for further investigation of the untrendy nature of oil price.