Analytical Solutions to Fractional Riccati Differential Economic Models with Memory Effects

Abstract

Fractional differential equations are highly beneficial in economics because they can be used to analyze nonlinear systems with memory effects. This research investigates a group of nonlinear fractional Riccati equations that show up in models of inventory and economic growth. The present work is a combined semi-analytical method for finding deterministic series solutions in the Caputo sense: the Adomian Decomposition–Sumudu Transform Method. Limited studies have examined its usage in memory-affected economic models. This method is effective with nonlinearities due to its ability to operate without the necessity of linearizing or discretizing them. The Mittag-Leffler function is employed to demonstrate that the series converges in a strict manner if it converges in a manner that is both absolute and uniform when the conditions are met. Finally, a Lyapunov stability study is conducted to ensure that the solution can accommodate modifications to the original data. Numerical models with different fractional orders show that the behavior of the system is controlled by the fractional parameter. When the fractional order is small, memory effects are increasing. As the order approaches closer to one, the solutions start to act like classical ones. These results indicate that the current methodology can be used for practical applications such as short-term currency exchange rates and volatility in financial markets.