The Lyapunov–Krasovskii theorem for a delayed conformable fractional system

This paper investigates a method for assessing conformable fractional-order systems with constant delays that is based on the Lyapunov–Krasovskii theorem. A novel asymptotic stability criterion for linear conformable fractional systems that depend on delay has been developed by using relevant mathematical inequalities and constructing an appropriate Lyapunov–Krasovskii functional. The proposed results offer practical tools for system analysis and design, extending classical stability theory to fractional-delay systems. The simplicity and efficacy of the suggested method have been illustrated with numerical examples. These results advance the theoretical understanding of conformable fractional systems and provide practical tools for stability assessment. Finally, numerical examples and computer simulations have shown the results’ applicability.