Stability analysis of fractional differential time-delay equations

This study provides a novel analytical approach to studying the solutions and stability of fractional differential delay equations without using Lyapunov function method. By applying the properties of Caputo fractional derivatives, the Laplace transform and the Mittag-Leffler function, the authors first provide an explicit formula and solution bounds for the solutions of linear fractional differential delay equations. Then, they prove new sufficient conditions for exponential boundedness, asymptotic stability and finite-time stability of such equations. The results are illustrated by numerical examples.