STABILITY ANALYSIS OF ECONOMIC PROCESSES USING FRACTIONAL-ORDER DIFFERENTIAL EQUATIONS

Abstract

This article presents a rigorous mathematical and computational study on the application of fractional-order differential equations to analyze the stability of complex economic processes. Unlike classical models, which assume instantaneous responses to economic shocks, fractional calculus introduces memory and hereditary properties that more accurately reflect real-world systems. The study employs Caputo and Riemann–Liouville derivatives to construct dynamic models of capital accumulation, inflation, and investment growth, enabling a more realistic simulation of delayed market responses. Using Lyapunov stability theory and numerical solutions via the Grünwald–Letnikov scheme, the paper explores how fractional-order parameters influence economic stability and bifurcation behavior. The results indicate that the inclusion of fractional derivatives smooths abrupt transitions, reduces oscillations, and provides a better understanding of the self-regulating nature of economic systems. This research bridges applied mathematics and economics by demonstrating how fractional dynamics offer a unified framework for modeling, prediction, and stability control.