Stability Analysis of Fractional Chaotic and Fractional-Order Hyperchain Systems Using Lyapunov Functions (European Journal of Pure and Applied Mathematics, 2025)
This study investigates the stability of nonlinear systems, particularly those characterized by eigenvalues. We introduce dynamic Lyapunov functions as a mechanism for stability analysis, especially when explicit solutions are not available. The authors provide stability criteria at the equilibrium point, demonstrating exponential stability and ensuring a return to equilibriumfollowing disturbances. The results have a big effect on the design and analysis of control systems because they provide a new way to achieve stability without using complicated calculations or assumptions. The abstract delineates the Riemann–Liouville fractional integral, Caputo fractional integrals and derivatives, and the Mittag–Leffler function. The research employs the root–Horwitz criteria and introduces a novel formulation of the superchaotic Chen system. Fractional superchain systems (FHCS) represent a sophisticated framework for investigation.
Keywords: Caputo Derivatives; Mittag-Leffler function; Hurwitz matrices; stability analysis; hyperchain systems