Economic growth (GDP) Model of India using fractional differential equation

Abstract

Economic growth modeling has long been a fundamental aspect of macroeconomic analysis, with GDP serving as a key indicator of national economic performance. Traditional growth models, such as the Solow-Swan model, typically assume a deterministic framework, while stochastic variations introduce randomness to account for economic fluctuations. However, recent advancements in fractional calculus have provided new tools for refining economic models by incorporating memory effects and long-range dependencies, which are particularly relevant for complex economic systems like India. This study explores the application of fractional differential equations in modeling India’s GDP growth by extending both the classical Solow-Swan model and its stochastic counterpart into a fractional domain. By leveraging fractional differentiation, the model captures persistent growth trends and dynamic adjustments with greater flexibility compared to integer-order models. Empirical validation is conducted using historical GDP data of India, applying numerical methods to solve the proposed fractional models. A comparative analysis of deterministic, stochastic, and fractional models is performed to assess their predictive accuracy and stability. The findings suggest that fractional-order models offer superior adaptability in capturing economic fluctuations and long-term dependencies, making them a valuable tool for economic forecasting and policy formulation. The study highlights the practical implications of fractional economic modeling and suggests avenues for further research in macroeconomic applications.