A Novel Fractional-Order Grey Model: Development and Application in R&D Expenditure Prediction

The interplay between economic growth and technological advancement creates a mutually reinforcing cycle, where economic development stimulates scientific progress while technological innovations accelerate the dissemination of information technologies. This symbiotic relationship underscores the critical importance of sustained investment in scientific innovation. This study introduces a novel fractional-order accumulation model (FOGM(1,N)) that innovatively applies distinct fractional-order accumulation operations to both independent and dependent variables. By extending the conventional integer-order calculus to fractional-order calculus, the proposed framework significantly enhances model flexibility and expands its potential applications. To address the computational challenges posed by the nonlinear nature of the objective function, we employ Genetic Algorithms for parameter optimization, thereby improving model precision through sophisticated computational techniques. For empirical validation, we selected research and development expenditure data from two Chinese provinces (Hunan and Zhejiang) as case studies. Comparative analysis demonstrates that the FOGM(1,N) model achieves superior predictive accuracy compared to conventional models, with mean absolute percentage errors reduced to 2% across test scenarios. These findings not only confirm the model's enhanced performance but also suggest its broader applicability in complex socioeconomic system modeling.