A Fractional Calculus Approach to Two-Variable Function Modeling of GDP Growth Rates: Evidence from G8 Countries and Türkiye

This study proposes a two-variable fractional calculus–based modeling framework for analyzing gross domestic product (GDP) growth rates using key macroeconomic indicators of G8 countries and Türkiye over the period of 1998–2022. The economic variables considered include exports, imports, inflation, foreign direct investment, and unemployment rates, with data obtained from the World Bank. Caputo-type fractional derivatives combined with the least squares method are employed to construct two-variable economic models, where GDP growth rate is treated as the dependent variable. Multiple combinations of economic factors are systematically examined to evaluate their modeling performance. The accuracy of the proposed models is assessed using the Mean Absolute Percentage Error (MAPE). The results indicate that the export–inflation combination yields the lowest modeling error for Japan, while the inflation–unemployment combination produces the highest error for Russia. Overall, the findings demonstrate that fractional calculus–based bivariate models provide an effective and flexible framework for capturing nonlinear and memory-dependent dynamics in economic growth analysis.