A fractional-order financial model: dynamics and stability analysis

This paper presents a fractional-order financial model integrating interest rates, investment demand, and price dynamics. The model is formulated as a three-dimensional system of Caputo fractional differential equations involving key economic parameters for saving amount, investment cost, elasticity of demand, A government control parameter to model economic stimulus and time varying critical rate to account for periodic economic shocks or policy cycles. Stability analysis via linearization and eigenvalue techniques confirms the local stability of the set of some equilibrium points. Notably, the fractional order α∈(0,1] introduces memory effects, expanding the system’s dynamic behavior beyond classical models. Existence of solution of governing equations model is provided using Banach fixed point theorem. Numerical simulations indicate conditional stability under the criterion |arg(λi)|>απ/2, and reveal cyclical patterns driven by complex eigenvalue pairs. These findings highlight the nuanced influence of fractional derivatives in financial modeling.