A caputo fractional order financial mathematical model analyzing the impact of an adaptive minimum interest rate and maximum investment demand

Abstract

A key model for predictive analysis, particularly in finance, is the Rössler system. This study introduces an enhanced version of this model, incorporating minimum interest rates and maximum investment demands. To capture its temporal dynamics, we used the Caputo fractional order derivative, which allowed us to evaluate the memory effect that underpins these factors’ financial stability and volatility over time. The research establishes the existence and uniqueness of the model solution, confirming its reliability. Numerical solutions obtained via the homotopy perturbation method and simulations reveals a positive correlation between maximum investment demand and interest rates, highlighting the significant impact of long-term dependencies and non-local influences of demands on interest rates. The insights provide valuable guidance for navigating financial uncertainties and optimizing investment strategies for market stability, deepening our understanding of relationships in nonlinear financial systems.