Stability Analysis of Fractional Order Differential Equations with Time Delays

Abstract

This paper investigates the stability characteristics of fractional order differential equations (FODEs) incorporating time delays. Using the Lyapunov-Krasovskii method, we derive sufficient conditions for the stability of solutions to these delayed fractional systems. The theoretical findings are applied to several examples, including models of population dynamics and engineering systems. Numerical simulations validate the theoretical results, demonstrating the role of time delays in system behavior and stability.