A novel fractional-order kernel regularized non-homogeneous grey Riccati model and its application in oil reserves prediction

Oil is an important energy source and industrial raw material that has profound impacts on the world's economy, politics, environment, and society. Therefore, accurate prediction of oil reserves can provide significant assistance to countries in terms of oil extraction, price adjustments, and the formulation of other energy policies. In this regard, this article proposes a novel fractional-order nuclear regularized non-homogeneous grey Riccati prediction model. The novel grey model synergistically combines the Hausdorff fractional-order accumulation operator and Grunwald-Letnikov fractional-order derivative, resulting in increased flexibility and streamlined computational procedures. The temporal response function and recursive formulation of this novel model are obtained by employing the forward difference technique. The recursive relationship between binomials in the discrete solution avoids function computation, simplifying the calculations. Nonlinear terms and a combination represented by Lagrange multipliers and kernel functions are introduced to simulate the nonlinearity and volatility characteristics of petroleum reserves, enhancing the adaptability of the grey prediction model to nonlinear and volatile time series. Through comparative experiments designed with optimization algorithms, the model exhibits high flexibility and strong adaptability. To illustrate the model's performance, two examples of petroleum reserve prediction compare the new model with traditional GM(1,1) grey model, fractional-order grey model, and kernel-based grey model. Based on the experimental results, it is evident that the proposed model surpasses other rival models in terms of fitting accuracy and prediction precision. Monte Carlo simulation and probability density analysis further indicate the model's good predictive performance and high robustness. Based on these prediction results, relevant recommendations can be provided to decision-makers for future oil extraction and utilization.